Premium
A parallel implicit domain decomposition algorithm for the large eddy simulation of incompressible turbulent flows on 3D unstructured meshes
Author(s) -
Liao ZiJu,
Chen Rongliang,
Yan Zhengzheng,
Cai XiaoChuan
Publication year - 2018
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4695
Subject(s) - jacobian matrix and determinant , domain decomposition methods , polygon mesh , discretization , solver , computer science , large eddy simulation , algorithm , discontinuous galerkin method , mathematics , finite element method , turbulence , mathematical optimization , geometry , mathematical analysis , physics , mechanics , thermodynamics
Summary We present a parallel fully implicit algorithm for the large eddy simulation (LES) of incompressible turbulent flows on unstructured meshes in three dimensions. The LES governing equations are discretized by a stabilized Galerkin finite element method in space and an implicit second‐order backward differentiation scheme in time. To efficiently solve the resulting large nonlinear systems, we present a highly parallel Newton‐Krylov‐Schwarz algorithm based on domain decomposition techniques. Analytic Jacobian is applied in order to obtain the best achievable performance. Two benchmark problems of lid‐driven cavity and flow passing a square cylinder are employed to validate the proposed algorithm. We then apply the algorithm to the LES of turbulent flows passing a full‐size high‐speed train with realistic geometry and operating conditions. The numerical results show that the algorithm is both accurate and efficient and exhibits a good scalability and parallel efficiency with tens of millions of degrees of freedom on a computer with up to 4096 processors. To understand the numerical behavior of the proposed fully implicit scheme, we study several important issues, including the choices of linear solvers, the overlapping size of the subdomains, and, especially, the accuracy of the Jacobian matrix. The results show that an exact Jacobian is necessary for the efficiency and the robustness of the proposed LES solver.