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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A weighted state redistribution algorithm for embedded boundary grids

State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions. Second, we discuss several algorithmic changes and improvements motivated by the more complicated cut cell geometries that can occur in higher dimensions. In particular, we introduce a weighted version with less dissipation in an easily generalizable framework. Third, we demonstrate that state redistribution can also stabilize a solution update that includes both advective and diffusive contributions. Notably, the stabilization algorithm is shown to be effective for incompressible as well as compressible reacting flows. Finally, we discuss the implementation of the algorithm for several exascale-ready simulation codes based on AMReX, demonstrating ease of use in combination with domain decomposition, hybrid parallelism and complex physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Moving Embedded Boundary Approach for the Compressible Navier-Stokes Equations in a Block-Structured Adaptive Refinement Framework

A computational technique has been developed to perform compressible flow simulations involving moving boundaries using an embedded boundary approach within the block-structured adaptive mesh refinement (SAMR) framework of AMReX [1], [91], [92]. We leverage the SAMR capability to obtain quantitatively accurate results whilst using robust, second-order finite volume schemes. A conservative, unsplit, cut-cell approach is utilized and a ghost-cell approach is developed for computing the flux on the moving, embedded boundary faces. A third-order least-squares formulation has been developed to compute the wall velocity gradients, and was found to significantly improve the performance of the solver in terms of the quantitative comparison of surface quantities such as the skin friction coefficient. Various test cases are performed to validate the method, and compared with analytical, experimental, and other numerical results in literature. Inviscid and viscous test cases are performed that span a wide regime of flow speeds - acoustic (harmonically pulsating sphere), smooth flows (expansion fan created by a receding piston) and flows with shocks (shock-cylinder interaction, shock-wedge interaction, pitching NACA 0012 airfoil and shock-cone interaction). A closed system with moving boundaries - an oscillating piston in a cylinder, showed that the percentage error in mass within the system decreases with refinement, demonstrating that the numerical scheme is conservative with grid refinement, but is not discretely conservative. Viscous test cases involve that of a horizontally moving cylinder at Re = 40, an inline oscillating cylinder at Re = 100, and a transversely oscillating cylinder at Re = 185. The judicious use of adaptive mesh refinement with appropriate refinement criteria to capture the regions of interest leads to well-resolved flow features, and good quantitative comparison is observed with the results available in literature.

adaptive refinement↗
DOE OSTI2022

High-order dimensionally-split Cartesian embedded boundary method for non-dissipative schemes

Centered finite-difference schemes are commonly used for high-fidelity turbulent flow simulations in canonical configurations because of their non-dissipative property and computational efficiency. However, their use in flow simulations over complex geometries is limited by the requirements of a structured grid and a stable boundary treatment in the absence of artificial (numerical) dissipation. Cartesian embedded boundary (EB) approaches provide an efficient structured-grid framework to apply difference schemes over complex domains. However, they are often restricted to low orders of accuracy because of numerical instabilities at the embedded boundaries and the issues of small-cell problem that are difficult to address with high-order accuracy. The present work discusses a systematic approach to obtain high-order EB methods with non-dissipative centered schemes in the interior. This approach, based on satisfying the primary and secondary conservation conditions, is employed to derive EB schemes that are up to sixth-order accurate in the interior and fourth-order accurate globally for hyperbolic, parabolic as well as incompletely parabolic problems. The proposed finite-difference discretization is, by construction, dimensionally split and addresses the small-cell problem without any cell/geometry transformations, thus, highly simplifying implementation in a flow solver. Various linear and non-linear numerical tests are performed to evaluate the stability and the accuracy of the proposed EB schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Fourth-Order Embedded Boundary Finite Volume Method for the Unsteady Stokes Equations with Complex Geometries

A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the ``small cut-cell"" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. In conclusion, the developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics

Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. In conclusion, we present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2000

A Domain-Decomposed Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.

Aftosmis, M. J.↗
DOE OSTI2025

Using AMReX's Embedded Boundaries to Support MFIX-Exa’s Geometry Capabilities

MFIX-Exa is an AMReX-based application used for the simulation of chemically reacting multiphase flows inside reactors. The reactor geometry is mostly a combination of primitive shapes such as cylinders, cubes and spheres of varying dimensions connected together with potentially a lot of dead space between them. Additionally, the reactors may have particle-laden jets introduced at different parts of their geometry to enhance reactant mixing. This talk presents how MFIX-Exa uses OpenSCAD’s csg format to allow users to define the embedded boundary (EB) geometry and how it supports specifying inflow through certain sections of the EB. The talk will describe how MFIX-Exa leverages the EB features of grid-pruning, restart files and redistribution. Finally, the talk goes over some capabilities which are currently not available in MFIX-Exa but planned for the future, such as moving parts of the reactor geometry.

embedded boundaries↗
DOE OSTI2025

Pore Resolved Simulations of Joule Heating in Fibrous Media using an Embedded Boundary Method

Joule heating has been regarded as an energy-efficient and sustainable method for heating materials and gases at large scales. The modeling of local temperature effects at pore-resolved scales for such systems, however, has been difficult to achieve due to challenges in coupling thermo-chemical processes in complex porous media and in large representative volume elements (RVEs). To this end, we developed an electro-thermal model at the pore scale to study Joule heating effects in large heterogeneous systems with different microstructures. This was achieved using the level set method to implicitly delineate distinct regions within the domain, and an embedded boundary method to facilitate heat exchange across the fluid-solid interface. Moreover, we applied this method to investigate unsteady non-linear electro-thermal effects in non-woven fibrous graphite conductors for RVEs with characteristic lengths of 2 mm, with different fiber orientations, porosity (80% – 90%) and fiber diameters (10 – 20µm). The coupled equations were solved numerically and they produced peak temperatures greater than 2000 K resulting in heating rates as high as 80,000 K/s. Moreover, the results depended strongly on the microstructure of the fiber skeleton and current density. Geometries with large fibers (∼ 20µm) had the highest average and peak temperatures with the mean temperature increasing by 3.9 % while the peak temperature increased by 9.9 %. Anisotropic domains on the other hand had the lowest mean and peak temperatures with peak and mean temperatures of 2293 K and 1437.7K respectively representing a corresponding 12.1% and 5.1% drop in the temperatures. An increase in porosity from 80% to 90%, however, led to an increase in the peak temperature by 5.1%.

Joule heating↗
NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗
NASA NTRS1998

A Domain-Decomposed Multi-Level Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

The work presents a new method for on-the-fly domain decomposition technique for mapping grids and solution algorithms to parallel machines, and is applicable to both shared-memory and message-passing architectures. It will be demonstrated on the Cray T3E, HP Exemplar, and SGI Origin 2000. Computing time has been secured on all these platforms. The decomposition technique is an outgrowth of techniques used in computational physics for simulations of N-body problems and the event horizons of black holes, and has not been previously used by the CFD community. Since the technique offers on-the-fly partitioning, it offers a substantial increase in flexibility for computing in heterogeneous environments, where the number of available processors may not be known at the time of job submission. In addition, since it is dynamic it permits the job to be repartitioned without global communication in cases where additional processors become available after the simulation has begun, or in cases where dynamic mesh adaptation changes the mesh size during the course of a simulation. The platform for this partitioning strategy is a completely new Cartesian Euler solver tarcreted at parallel machines which may be used in conjunction with Ames' "Cart3D" arbitrary geometry simulation package.

Aftosmis, M. J.↗
NASA NTRS2002

Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries

This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.

Aftosmis, M. J.↗
NASA NTRS2004

Adjoint Formulation for an Embedded-Boundary Cartesian Method

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.

Nemec, Marian↗
DOE OSTI2024

A new re-redistribution scheme for weighted state redistribution with adaptive mesh refinement

State redistribution (SRD) is a recently developed technique for stabilizing cut cells that result from finite-volume embedded boundary methods. SRD has been successfully applied to a variety of compressible and incompressible flow problems. When used in conjunction with adaptive mesh refinement (AMR), additional steps are needed to preserve the accuracy and conservation properties of the solution if the embedded boundary is not restricted to a single level of the mesh hierarchy. In this work, we extend the weighted state redistribution algorithm to cases where cut cells live at or near a coarse-fine interface within the domain. Here, we present numerical results that demonstrate that the algorithm is conservative when the coarse-fine interface intersects the embedded boundary. Additionally we compare the numerical solution of the Sod shock tube problem in an inclined cylinder with the analytic solution, and we compare the simulation of a shock hitting a cylindrical obstacle with experimental data. Finally we demonstrate the methodology for simulation of the multicomponent compressible Navier-Stokes equations in a piston-bowl geometry, and discuss the computational efficiency gained by not requiring the entire embedded boundary to be defined at the finest level.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Smoothed boundary method for simulating incompressible flow in complex geometries

Simulating flow through porous media with explicit considerations of complex microstructures is very challenging using conventional sharp-interface methods because of the difficulties in generating meshes conformal to complex geometries. In this work, a diffuse interface embedded boundary method known as the Smoothed Boundary Method (SBM) is utilized to facilitate simulations of fluid dynamics involving complex geometries. In diffuse-interface methods, the geometry is described by a domain parameter. The SBM allows the straightforward reformulation of the time-dependent Navier-Stokes equations in terms of this domain parameter, using only algebraic identities. Thus, enforcing the appropriate boundary conditions at the irregular embedded boundary is greatly simplified. Adaptive mesh refinement is used to increase the accuracy of the diffuse interface method by allowing thinner interfacial thickness to be used in the domain parameter. Here, the SBM-formulated Navier-Stokes equations are solved with the Finite Difference Method on refined mesh systems. Sharp-interface Finite Element Method simulations using the commercial software COMSOL on body-conforming meshes are also provided for comparison. Favorable agreement between the two methods is observed. Since it is no longer necessary for the mesh to conform to the complex geometry, the grid system for the SBM simulations can be generated rapidly and without additional manual interventions, making the entire simulation process more expedient.

36 MATERIALS SCIENCE↗