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DOE OSTI2020

Code-to-code-to-experiment validation of LES-ALM wind farm simulators

The aim of this work is to present a detailed code-to-code comparison of two Large-Eddy Simulation (LES) solvers. Corresponding experimental measurements are used as a reference to validate the quality of the CFD simulations. The comparison highlights the effects of solver order on the solutions, and it tries to answer the question of whether a high order solver is necessary to capture the main characteristics of a wind farm. Both solvers were used on different grids to study their convergence behavior. While both solvers show a good match with experimental measurements, it appears that the low order solver is more accurate and substantially cheaper in terms of computational cost.

17 WIND ENERGY↗

DOE OSTI2024

Grid Optimization Competition Challenge 3 Problem Formulation

This report contains the problem formulation for the Grid Optimization (GO) Competition Challenge 3. The Grid Optimization Competition is run by a team of researchers from a number of organizations, including the sponsor Advanced Research Projects Agency - Energy (ARPA-E), lead organization Pacific Northwest National Laboratory (PNNL), and technical contributors from Los Alamos National Laboratory (LANL), National Renewable Energy Laboratory (NREL), Texas A&M University (TAMU), Georgia Institute of Technology (GT), University of Wisconsin (UW), and others. The GO Competition poses challenge problems in the field of power grid management, invites entrants to develop solvers for these problems, invokes the solvers on a set of problem instances using common hardware, ranks the solvers according to their performance, and awards prizes according to the rankings. The overall goal of the GO Competition is to spur innovative research on high impact and computationally challenging problems in power grid management from initial development through commercial deployment. Complete information about the GO Competition can be found online at [2]. The webpage covers previous Challenges, rules, timeline, registration information, data formats, scoring methods, computational platform information, information on supported solvers and languages, sponsor information, frequently asked questions, administrator contact information, publicly available problem instances, computer code for reading and evaluating problem and solution data, a sandbox for testing solvers, and a solver submission interface, results, and publications.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

INTEGRATE - Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements

The INTEGRATE (Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements) project is developing a new inverse-design capability for the aerodynamic design of wind turbine rotors using invertible neural networks. This AI-based design technology can capture complex non-linear aerodynamic effects while being 100 times faster than design approaches based on computational fluid dynamics. This project enables innovation in wind turbine design by accelerating time to market through higher-accuracy early design iterations to reduce the levelized cost of energy. INVERTIBLE NEURAL NETWORKS Researchers are leveraging a specialized invertible neural network (INN) architecture along with the novel dimension-reduction methods and airfoil/blade shape representations developed by collaborators at the National Institute of Standards and Technology (NIST) learns complex relationships between airfoil or blade shapes and their associated aerodynamic and structural properties. This INN architecture will accelerate designs by providing a cost-effective alternative to current industrial aerodynamic design processes, including: - Blade element momentum (BEM) theory models: limited effectiveness for design of offshore rotors with large, flexible blades where nonlinear aerodynamic effects dominate - Direct design using computational fluid dynamics (CFD): cost-prohibitive - Inverse-design models based on deep neural networks (DNNs): attractive alternative to CFD for 2D design problems, but quickly overwhelmed by the increased number of design variables in 3D problems AUTOMATED COMPUTATIONAL FLUID DYNAMICS FOR TRAINING DATA GENERATION - MERCURY FRAMEWORK The INN is trained on data obtained using the University of Marylands (UMD) Mercury Framework, which has with robust automated mesh generation capabilities and advanced turbulence and transition models validated for wind energy applications. Mercury is a multi-mesh paradigm, heterogeneous CPU-GPU framework. The framework incorporates three flow solvers at UMD, 1) OverTURNS, a structured solver on CPUs, 2) HAMSTR, a line based unstructured solver on CPUs, and 3) GARFIELD, a structured solver on GPUs. The framework is based on Python, that is often used to wrap C or Fortran codes for interoperability with other solvers. Communication between multiple solvers is accomplished with a Topology Independent Overset Grid Assembler (TIOGA). NOVEL AIRFOIL SHAPE REPRESENTATIONS USING GRASSMAN SPACES We developed a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation as an analytic generative model, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data , (ii) improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes. TECHNOLOGY TRANSFER DEMONSTRATION - COUPLING WITH NREL WISDEM Researchers have integrated the inverse-design tool for 2D airfoils (INN-Airfoil) into WISDEM (Wind Plant Integrated Systems Design and Engineering Model), a multidisciplinary design and optimization framework for assessing the cost of energy, as part of tech-transfer demonstration. The integration of INN-Airfoil into WISDEM allows for the design of airfoils along with the blades that meet the dynamic design constraints on cost of energy, annual energy production, and the capital costs. Through preliminary studies, researchers have shown that the coupled INN-Airfoil + WISDEM approach reduces the cost of energy by around 1% compared to the conventional design approach. This page will serve as a place to easily access all the publications from this work and the repositories for the software developed and released through this pr...

aerodynamics↗

NASA NTRS1993

Computational flow predictions for hypersonic drag devices

The effectiveness of two types of hypersonic decelerators is examined: mechanically deployable flares and inflatable ballutes. Computational fluid dynamics (CFD) is used to predict the flowfield around a solid rocket motor (SRM) with a deployed decelerator. The computations are performed with an ideal gas solver using an effective specific heat ratio of 1.15. The results from the ideal gas solver are compared to computational results from a thermochemical nonequilibrium solver. The surface pressure coefficient, the drag, and the extend of the compression corner separation zone predicted by the ideal gas solver compare well with those predicted by the nonequilibrium solver. The ideal gas solver is computationally inexpensive and is shown to be well suited for preliminary design studies. The computed solutions are used to determine the size and shape of the decelerator that are required to achieve a drag coefficient of 5. Heat transfer rates to the SRM and the decelerators are predicted to estimate the amount of thermal protection required.

Tokarcik, Susan A.↗

NASA NTRS2007

USM3D Unstructured Grid Solutions for CAWAPI at NASA LaRC

In support the Cranked Arrow Wing Aerodynamic Project International (CAWAPI) to improve the Technology Readiness Level of flow solvers by comparing results with measured F-16XL-1 flight data, NASA Langley employed the TetrUSS unstructured grid solver, USM3D, to obtain solutions for all seven flight conditions of interest. A newly available solver version that incorporates a number of turbulence models, including the two-equation linear and non-linear k-epsilon, was used in this study. As a first test, a choice was made to utilize only a single grid resolution with the solver for the simulation of the different flight conditions. Comparisons are presented with three turbulence models in USM3D, flight data for surface pressure, boundary-layer profiles, and skin-friction results, as well as limited predictions from other solvers. A result of these comparisons is that the USM3D solver can be used in an engineering environment to predict flow physics on a complex configuration at flight Reynolds numbers with a two-equation linear k-epsilon turbulence model.

Lamar, John E.↗

NASA NTRS2009

Numerical Solutions for the CAWAPI Configuration on Unstructured Grids at NASA LaRC, United States

In support of the Cranked Arrow Wing Aerodynamic Project International (CAWAPI) with its goal of improving the Technology Readiness Level of flow solvers by comparing results with measured F-16XL-1 flight data, NASA Langley employed the TetrUSS unstructured grid solver, USM3D, to obtain solutions for all seven flight conditions of interest. A newly available solver version that incorporates a number of turbulence models, including the two-equation linear and non-linear k- , was used in this study. As a first test, a choice was made to utilize only a single grid resolution with the solver for the simulation of the different flight conditions. Comparisons are presented with three turbulence models in USM3D, flight data for surface pressure, boundary-layer profiles, and skin-friction distribution, as well as limited predictions from other solvers. A result of these comparisons is that the USM3D solver can be used in an engineering environment to predict vortex-flow physics on a complex configuration at flight Reynolds numbers with a two-equation linear k- turbulence model.

Lamar, John E.↗

NASA NTRS2013

Recent Advances in Agglomerated Multigrid

We report recent advancements of the agglomerated multigrid methodology for complex flow simulations on fully unstructured grids. An agglomerated multigrid solver is applied to a wide range of test problems from simple two-dimensional geometries to realistic three- dimensional configurations. The solver is evaluated against a single-grid solver and, in some cases, against a structured-grid multigrid solver. Grid and solver issues are identified and overcome, leading to significant improvements over single-grid solvers.

Nishikawa, Hiroaki↗

NASA NTRS2018

LAVA Simulations for the 3rd AIAA CFD High Lift Prediction Workshop with Body Fitted Grids

In response to the 3rd AIAA CFD High Lift Prediction Workshop, the workshop cases were analyzed using Reynolds-averaged Navier-Stokes flow solvers within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework. For the workshop cases the advantages and limitations of both overset-structured an unstructured polyhedral meshes were assessed. The workshop included 3 cases: a 2D airfoil validation case, a mesh convergence study using the High Lift Common Research Model, and a nacelle/pylon integration study using the JAXA (Japan Aerospace Exploration Agency) Standard Model. The 2D airfoil case from the workshop is used to verify the implementation of the Spalart-Allmaras turbulence model along with some of its variants within the solver. The High Lift Common Research Model case is used to assess solver performance and accuracy at varying mesh resolutions, as well as identify the minimum mesh fidelity required for LAVA on this class of problem. The JAXA Standard Model case is used to assess the solver's sensitivity to the turbulence model and to compare the structured and unstructured mesh paradigms. These workshop cases have helped establish best practices for high lift flow configurations for the LAVA solver.

LAVA↗

NASA NTRSDate not supplied

Exploring Airfoil Table Generation using XFOIL and OVERFLOW

The rotorcraft design process is a continuously evolving field of research that incorporates a number of software programs. An accurate airfoil table is critical in the design and testing process for rotorcraft. With multiple flow solvers available and flow conditions of multirotor UAM vehicles potentially covering a wide range of Reynolds and Mach numbers, a documented approach for developing airfoil tables is needed. Using benchmark data from legacy airfoil tables and wind tunnel tests for comparison, simulations for a comprehensive test matrix could guide rotorcraft design engineers in generating their own airfoil tables using the XFOIL and OVERFLOW solvers. The motivation for this study is to investigate flow solver features to develop a best practices document for airfoil table generation. The study uses the OVERFLOW and XFOIL flow solvers, coupled with the airfoil table generator AFTGen, to analyze three airfoils for a specific Reynolds numbers flow regime and provide details on how well each flow solver performs within a specific angle of attack range, Mach number range, Reynolds number range, and in different flow conditions, such as turbulent and transitional flow. OVERFLOW analyses in AFTGen for fully turbulent and transition flow are compared with XFOIL results and experimental test data for the section lift, section drag, and pressure coefficients. XFOIL ultimately yields results that are accurate within the linear angle of attack range and below a Mach number of 0.4 but tends to overpredict lift and underpredict drag unless the flow is in the compressible regime. XFOIL cannot accurately model stall and post-stall conditions due to the nature of the solver. This is evident in nearly every case run with XFOIL, where the linear range is usually predicted acceptably and the lift coefficient is overpredicted as the stall angle of attack is approached (with the exception being the generally poor correlation with most of the SSC-A09 cases). OVERFLOW is limited at low Mach numbers, and appears to perform best at Mach numbers of 0.4 and above. The exploration of airfoil table generation using XFOIL and OVERFLOW yielded moderately successful results for the NACA 0012 airfoil, reasonably good results for the RC(4)-10 airfoil, and less accurate results for the SSC-A09 airfoil.

Airfoil Table Generation↗

NASA NTRSDate not supplied

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO). PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Material Response↗

NASA NTRSDate not supplied

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗

DOE OSTI2022

Development of a calculation framework coupling Monte Carlo neutronics, subchannel thermal-hydraulics and 1.5D fuel thermo-mechanics

A coupled calculation system consisting of the Monte Carlo neutronic solver SERPENT and the fuel behaviour solver TRANSURANUS was extended with the sub-channel thermal-hydraulic solver SUBCHANFLOW to form a coupled calculation framework for multi-physics reactor analyses. The coupling between the 3 solvers was accomplished via a driver program written in Perl that runs the solvers, processes and transfers the output data between the solvers and monitors the convergence. While some features of the coupling are still under development, a steady-state coupled calculation resulting in convergence was performed for a single hexagonal fuel assembly to demonstrate that the base functionalities work as expected. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Coupling of nTRACER to COBRA-TF for full core high-fidelity analysis of VVERs

The evolution of computing clusters allows the use of high-resolution multi-physics solvers for reactor analysis. Despite the continuous expansion of VVER technology, only one other high-fidelity sub-pin multi-physics core solver is currently developed for safety analysis. To that end the Laboratory of Reactor Physics and Thermal-Hydraulics (LRT) of Paul Scherrer Institut is developing such a tool with the coupling of the neutronic code nTRACER and the sub-channel code COBRA-TF. This work follows the initial steps of the coupling and focuses to the extension of the core solver to full core VVER geometries. The X2 VVER-1000 benchmark is modeled with the novel core solver. The results are compared to the ones of a standalone nTRACER calculation where the feedbacks are provided by a simplified 1D thermal-hydraulic solver. Despite relatively good agreement in power distribution, the limitations of the simplified solver become apparent especially when comparing global temperature profiles. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A computationally-efficient method for flamelet calculations

A new open-source code for the simulation of the diffusion flamelet equations is proposed. Emphasis is placed on using an approximate Jacobian to reduce the computational cost of the matrix operations. Performance of the proposed solvers is tested by performing flamelet calculations with kinetic mechanisms of varying sizes. For the unity Lewis number equations, the present iterative Newton solver using an approximate Jacobian greatly outperforms direct Newton solvers using exact Jacobians. The computation cost scales linearly with the number of species, leading to a reduction in solution times by two orders of magnitude for mechanisms containing thousands of species. The applicability of the Jacobian approximations to the solution of the non-unity Lewis number flamelet equations is assessed. The approximations are generally inadequate to solve the full non-unity Lewis number equations but can be used in some applications depending on the balance of terms in the flamelet equations. As an example, the flamelet solver is applied to the study of sooting tendencies in laminar co-flow diffusion flames where modified non-unity Lewis number flamelet equations, previously shown to accurately reproduce experimentally-measured Yield Sooting Indices (YSI), are solved. Here, the accelerated flamelet solver is well suited for sensitivity analysis and uncertainty quantification with large detailed kinetic mechanisms, tasks for which the computational cost was previously prohibitive.

42 ENGINEERING↗

DOE OSTI2024

Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media

A full approximation scheme (FAS) nonlinear multigrid solver for two-phase flow and transport problems driven by wells with multiple perforations is developed here. It is an extension to our previous work on FAS solvers for diffusion and transport problems. The solver is applicable to discrete problems defined on unstructured grids as the coarsening algorithm is aggregation-based and algebraic. To construct coarse basis that can better capture the radial flow near wells, coarse grids in which perforated well cells are not near the coarse-element interface are desired. This is achieved by an aggregation algorithm proposed in this paper that makes use of the location of well cells in the cell-connectivity graph. Numerical examples in which the FAS solver is compared against Newton's method on benchmark problems are given. In particular, for a refined version of the SAIGUP model, the FAS solver is at least 35% faster than Newton's method for time steps with a CFL number greater than 10.

58 GEOSCIENCES↗

DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗