Application of nonlinear Krylov acceleration to a reconstructed discontinuous Galerkin method for compressible flows

作者：Wang, Chuanjin; Cheng, Jian; Berndt, Markus; Carlson, Neil N.; Luo, Hong^*

来源：Computers & Fluids, 2018, 163: 32-49.

DOI：10.1016/j.compfluid.2017.12.015

• Nonlinear Krylov acceleration
• Reconstructed discontinuous Galerkin
• ESDIRK
• Compressible flows
• Euler equations
• Navier-Stokes

A variant of Anderson Mixing, namely the Nonlinear Krylov Acceleration (NKA), is presented and implemented in a reconstructed Discontinuous Galerkin (rDG) method to solve the compressible Euler and Navier-Stokes equations on hybrid grids. A nonlinear system of equations as a result of a fully implicit temporal discretization at each time step is solved using the NKA method with a lower-upper symmetric Gauss-Seidel (LU-SGS) preconditioner. The developed NKA method is used to compute a variety of flow problems and compared with a well-known Newton-GMRES method to demonstrate the performance of the NKA method. Our numerical experiments indicate that the NKA method outperforms its Newton-GMRES counterpart for transient flow problems, and is comparable to Newton-GMRES for steady cases, and thus provides an attractive alternative to solve the system of nonlinear equations arising from the rDG approximation.

• 出版日期2018-2-15
• 单位Los Alamos; 北京航空航天大学