An Evaluation of Implicit Time Integration Schemes for Discontinuous High Order Methods

Abstract

For many flow problems, implicit time integration schemes are known to achieve solution convergence in acceptable time, and significantly reduce the memory cost comparing with explicit schemes. Many implicit schemes have been developed recently for high-order discontinuous methods. However, it is unclear which is the most efficient, robust and general. We carry out a comparative study of several implicit time integration schemes with the Correction Procedure via Reconstruction (CPR) high-order discretization. These schemes include the Lower-Upper Symmetric Gauss-Seidel(LU-SGS), a matrix-free GMRES solver with LU-SGS as a preconditioner, and a GMRES linear equation solver with different preconditioners within PETSc (Portable, Extensible Toolkit for Scientific Computation). Through a series of numerical experiments, the performance of these implicit time integration schemes is evaluated for high-order methods.