Open AccessFully implicit multiple graphics processing units’ schemes for hypersonic flows with lower upper symmetric Gauss-Seidel preconditioner on unstructured non-orthogonal grids
Author(s) -
A. N. Bocharov,
Н. М. Евстигнеев,
O. I. Ryabkov
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1698/1/012023
Subject(s) - preconditioner , discretization , hypersonic speed , multigrid method , mathematics , mach number , navier–stokes equations , unstructured grid , finite volume method , computer science , iterative method , grid , mathematical optimization , mathematical analysis , geometry , partial differential equation , compressibility , physics , mechanics
The paper discusses the simulation of the hypersonic flow problems on unstructured grids using fully implicit scheme and the analysis of the orthogonal corrections on the quality of heat fluxes on the surfaces of the bodies subject to hypersonic flow. The governing equations are the Navier-Stokes equations for viscous calorically perfect gas. Second order finite volume discretization is applied to the problem on arbitrary unstructured grids with implicit temporal treatment. The problem is solved using the Newton-Raphson method. Such methods require the solution of large linear systems with iterative solvers and require a preconditioning operator to converge. In this paper a well known Lower-Upper Symmetric Gauss Seidel (LU-SGS) preconditioner is applied. The new method is based on the tricky reordering for the factored Jacobi matrix that allows one to execute block triangular matrix solvers on GPUs in parallel without the loss of algebraic properties of the original non-factored operator. Good convergence properties are demonstrated for large scale problems of external aerodynamics with implicit Courant number around 1000 - 10000 for flows with Mach number around 13-25. The influence of the non-orthogonal corretions on the fluxes for highly scewed anisotropic grids is demonstrated at Mach numbers around 20. It is shown that the non-orthogonality corrections are of the second infinitesimal order compared to the effects of the shock fix influence on the heat fluxes on the body.