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A conference was held on parallel computational fluid dynamics and produced related papers. Topics discussed in these papers include: parallel implicit and explicit solvers for compressible flow, parallel computational techniques for Euler and Navier-Stokes equations, grid generation techniques for parallel computers, and aerodynamic simulation om massively parallel systems.
A hybrid boundary element finite volume method for unsteady transonic flow computation has been developed. In this method, the unsteady Euler equations in a moving frame of reference are solved in a small embedded domain (inner domain) around the airfoil using an implicit finite volume scheme. The unsteady full-potential equation, written in the same frame of reference and in the form of the Poisson equation. is solved in the outer domain using the integral equation boundary element method to provide the boundary conditions for the inner Euler domain. The solution procedure is a time-accurate stepping procedure, where the outer boundary conditions for the inner domain are updated using the integral equation -- boundary element solution over the outer domain. The method is applied to unsteady transonic flows around the NACA0012 airfoil undergoing pitching oscillation and ramp motion. The results are compared with those of an implicit Euler equation solver, which is used throughout a large computational domain, and experimental data.
The development of two new unsteady wake-blade row aerodynamic interaction models and of a rotor-stator unsteady aerodynamic interaction model are outlined. The solutions of Adamczyk's average-passage flow model were used. The responses to the potential disturbances through a blade row were calculated using the MSUTC code. This code can run with and without the use of wall functions. The solver is an implicit finite volume method with flux Jacobians which are evaluated by the flux-vector splitting and the residual fluxes by the Roe's flux-difference splitting.
Pneumatic active control of asymmetric vortical flows around a slender pointed forebody is investigated using the three dimensional solution for the compressible thin-layer Navier-Stokes equation. The computational applications cover the normal and tangential injection control of asymmetric flows around a 5 degree semi-apex angle cone at a 40 degree angle of attack, 1.4 freestream Mach number and 6 x 10(exp 6) freestream Reynolds number (based on the cone length). The effective tangential angle range of 67.5 approaches minus 67.5 degrees is used for both normal and tangential ports of injection. The effective axial length of injection is varied from 0.03 to 0.05. The computational solver uses the implicit, upwind, flux difference splitting finite volume scheme, and the grid consists of 161 x 55 x 65 points in the wrap around, normal and axial directions, respectively. The results show that tangential injection is more effective than normal injection.
A multiphysics simulation capability has been developed that incorporates mutual interactions between aerodynamics, structural response from aero/thermal loading, ablation/pyrolysis, heating, and surface-to-surface radiation to perform high-fidelity, fully coupled aerothermoelastic ablation simulations, which to date had been unattainable. The multiphysics framework couples CHAR (a 3-D implicit charring ablator solver), Loci/CHEM (a computational fluid dynamics solver for high-speed chemically reacting flows), and Abaqus (a nonlinear structural dynamics solver) to create a fully coupled aerothermoelastic charring ablative solver. The solvers are tightly coupled in a fully integrated fashion to resolve the effects of the ablation pyrolysis and charring process and chemistry products upon the flow field, the changes in surface geometry due to recession upon the flow field, and thermal-structural analysis of the body from the induced aerodynamic heating from the flow field. The multiphysics framework was successfully demonstrated on a solid rocket motor graphite nozzle erosion application. Comparisons were made with available experimental data that measured the throat erosion during the motor firing. The erosion data is well characterized, as the test rig was equipped with a windowed nozzle section for real-time X-ray radiography diagnostics of the instantaneous throat variations for deducing the instantaneous erosion rates. The nozzle initially undergoes a nozzle contraction due to thermal expansion before ablation effects are able to widen the throat. A series of parameters studies were conducted using the coupled simulation capability to determine the sensitivity of the nozzle erosion to different parameters. The parameter studies included the shape of the nozzle throat (flat versus rounded), the material properties, the effect of the choice of turbulence model, and the inclusion or exclusion of the mechanical thermal expansion. Overall, the predicted results match the experiment very well, and the predictions were able to bound the data within acceptable limits.
This paper presents a numerical approach to calculating turbulent flows employing advanced turbulence models. The main features include a line-by-line Gauss-Seidel algorithm using Roe's approximate Riemann solver, TVD numerical schemes, implicit boundary conditions and a decoupled turbulence-model solver. Based on the problems tested so far, the method has consistently demonstrated its ability in offering accuracy, boundedness and a fast rate of convergence to steady-state solution.
This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Finally, additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner.
The alternating-direction-implicit finite-difference technique [G.R. Hadley, Opt. Lett. 19,84 (1994).
A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.
Improvements have been made to the implicit symmetric successive overrelaxation algorithm in the OVERFLOW 2.3 structured, overset grid, computational fluid dynamics flow solver. These improvements, consisting of implicit boundary conditions, improved flux Jacobian linearizations, and CFL number ramping, are a series of evolutionary changes to the linear solver that have resulted in increased nonlinear convergence rates and faster time to solution. A series of test cases are presented that demonstrate the effect of the changes through comparison with the original SSOR path and other linear solver implementations within OVERFLOW.
We propose a simplication of the face-averaged nodal-gradient (FANG) method for a cell-centered finite-volume Euler/Navier-Stokes solver on arbitrary grids, and compare it with other gradient methods for trouble-prone grids in two dimensions. The implementation of the FANG method is simplified by adding the face-neighbor cells of the cells around a node to a least-squares gradient stencil. The resulting method is stable for both triangular and quadrilateral grids. Although it increases the residual stencil for triangular grids, it allows the solver to work seamlessly for mixed grids and greatly simplifies the implementation, especially in three dimensions. For comparison, only explicit weighted/unweighted least-squares cell-centered and nodal gradient methods are considered. These gradients are used in both inviscid and viscous schemes, and we investigate their impact on the iterative convergence of an implicit defect-correction solver on difficult grids such as highly-curved-and-thin grids and highly distorted anisotropic grids. Finally, we will also consider a face-stencil-based limiter and compare it with a conventional cell-stencil-based limiter.
The approach to carrying out multi-discipline aerospace design studies in the future, especially in massively parallel computing environments, comprises of choosing (1) suitable solvers to compute solutions to equations characterizing a discipline, and (2) efficient optimization methods. In addition, for aerodynamic optimization problems, (3) smart methodologies must be selected to modify the surface shape. In this research effort, a 'direct' optimization method is implemented on the Cray C-90 to improve aerodynamic design. It is coupled with an existing implicit Navier-Stokes solver, OVERFLOW, to compute flow solutions. The optimization method is chosen such that it can accomodate multi-discipline optimization in future computations. In the work , however, only single discipline aerodynamic optimization will be included.
We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform inverse modified error analysis of the ODE-nets using unrolled implicit schemes for ease of interpretation. It is shown that training an ODE-net using an unrolled implicit scheme returns a close approximation of an inverse modified differential equation (IMDE). In addition, we establish a theoretical basis for hyperparameter selection when training such ODE-nets, whereas current strategies usually treat numerical integration of ODE-nets as a black box. We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss. This helps accelerate training while maintaining accuracy. Several numerical experiments are performed to demonstrate the advantages of the proposed algorithm compared to nonadaptive unrollings and validate the theoretical analysis. Here, we also note that this approach naturally allows for incorporating partially known physical terms in the equations, giving rise to what is termed “gray box” identification.
In this document, the Advanced Simulation and Computing (ASC) Transport Project’s Jayenne team presents evidence that the Los Alamos National Laboratory (LANL) Level 2 milestone statement, Demonstrate a new unstructured mesh IMC x-ray transport capability in LAP codes, due Q4 FY20, has been satisfied with the release and integration of the Jayenne team’s Implicit Monte Carlo (IMC) solver libraries into the lumos multiphysics solver. The Jayenne project’s software includes the algorithms and features prescribed by the milestone description. The lumos software is maintained by the Lagrangian Applications Project (LAP) along with the hydrodynamics code flag and operates under the same ASC program as Jayenne. A set of demonstration problems has been specified, executed, and analyzed.
This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.
This article presents the OpenMP parallelization of the preconditioning Jacobian assembly and right‐hand side residual evaluation in UEDGE. A continuation algorithm, utilizing the internal NKSOL implicit Jacobian‐Free Newton‐Krylov solver to efficiently scan physical parameters, is also presented. The implemented parallelization reduces the computational time for a benchmark scan run on 32 threads by compared to the serial version when using trained random forest regression models to identify the optimal decomposition of the system of equations. Random forest regression models applied to the UEDGE time‐dependent and continuation solver algorithms did not yield meaningful improvement in computational performance. A benchmark DIII‐D gas injection rate scan in the 0.35–0.75 kA interval, performed on a test cluster using the parallelized code and continuation solver, produced 1066 steady‐state solutions with a 22 s average wall‐clock computational time per steady‐state solution.
Scikit-SUNDAE provides Python bindings to SUNDIALS integrators. The implicit differential algebraic (IDA) solver and C-based variable-coefficient ordinary differential equations (CVODE) solver are both included. The name SUNDAE combines (SUN)DIALS and DAE, which stands for differential algebraic equations. Solvers specific to DAE problems are not frequently available in Python. An ordinary differential equation (ODE) solver is also included for completeness. ODEs can be categorized as a subset of DAEs (i.e., DAEs with no algebraic constraints). https://pypi.org/project/scikit-sundae
A recently developed axisymmetric implicit unsteady Euler equation solver has been applied to the calculation of solar wind flows past terrestrial planets. The primary emphasis of this paper is on the application of that computational technique to the calculation of the flow field properties of steady, axisymmetric, supersonic/hypersonic flows past blunt-nosed shapes characteristic of interplanetary solar wind flows past both magnetic and nonmagnetic planets. The purpose is to demonstrate both the accuracy and flexibility of this new technique as well as to present a novel application of such supersonic blunt-body procedures.