An Efficient Implicit High-order Flux Reconstruction Method by Automatic Differentiation using Operator Overloading for Flow Simulation on Unstructured Hexahedral Grids

An efficient implicit high-order flux reconstruction/correction procedure via reconstruction method (FR/CPR) is developed to solve the compressible Navier-Stokes equation on unstructured hexahedral grids. The convergence rate of the proposed solver is greatly improved compared to Lower-upper Symmetry Gauss Seidel (LU-SGS) method. The restart GMRES (restarted Generalized Minimal Residual) is used to tackle the linear system by FR/CPR temporal and spatial discretization, and an automatic differential (AD) by operator overloading is proposed to construct the Jacobian matrix of the discretization system. The effects of automatic differential on the convergence rate of the developed implicit scheme have been investigated. Inviscid and viscous test cases are performed to evaluate the performance of the developed implicit solver.