Application of nonlinear Krylov acceleration to a reconstructed discontinuous Galerkin method for compressible flows. (15th February 2018)

• Record Type: Journal Article
• Authors: Wang, Chuanjin; Cheng, Jian; Berndt, Markus; Carlson, Neil N.; Luo, Hong
• Is Part Of: Computers & fluids. Volume 163(2018)
• Page Start: 32
• Page End: 49
• Publication Date: 2018-02-15
• Subjects: Nonlinear Krylov acceleration -- Reconstructed discontinuous Galerkin -- ESDIRK -- Compressible flows -- Euler equations -- Navier-Stokes; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2017.12.015
• Languages: English
• ISSNs: 0045-7930

Abstract

Abstract: 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.