Fast Time Integration of Navier-Stokes Equations with an Exponential-Integrator Scheme

摘要

In this paper, the second-order exponential time-integrator scheme, named the Predictor-Corrector Exponential scheme (PCEXP), originally developed by S.-J. Li, etc, in AIAA-2017-0753 is successfully extended to solve the compressible Navier-Stokes equations over three-dimensional geometries with hybrid curved elements. The stiffness of viscous flows that leads to a severe time-step size restriction in the explicit methods is addressed in the PCEXP content using a nearly exact evaluation of the residual Jacobians. The second method of Bassi-Rebay (BR2) is employed to discretize the viscous terms with a discontinuous Galerkin method. A hybrid approach for accurately computing the analytical high-order viscous Jacobian matrices is presented and an efficient way to simplify the computation is discussed, resulting in a robust while fast exponential time-integration method. We evaluate the PCEXP scheme using several benchmark test cases to demonstrate its substantial speedup compared to the classical third-order TVD Runge-Kutta approach and comparable performance to the implicit backward Euler (BE) method with large time steps.