Efficient Implicit Method for a High-Order Flux Reconstruction Approach Using Modified Matrix-Free Defect Correction

抄録

An efficient implicit time integration method for high-order CFD using the flux reconstruction (FR) approach is studied. The formulation is based on the method called matrix-free defect correction on sub-cells (DECS), which considerably reduces the computational cost of the preconditioned block LU-SGS (BLU-SGS). However, the present method uses the exact FR formulation for the simplified viscous terms in the left-hand-side Jacobian, and it does not explicitly use sub-cell divisions as a result of using the finite-difference formula. The performance of the proposed method is compared with BLU-SGS and DECS. Reductions of the computation time for the convergence are not remarkable, but the slightly improved stability and reduced memory storage suggest the present method as a reliable alternative to the existing methods.