An efficient flux-vector-splitting implicit scheme for 2-D internal flow

Abstract

A one-step flux-vector-splitting implicit scheme has been developed successfully for solving the two-dimensional Euler and Navier-Stokes equations for internal compressible flow. A new approach is developed to construct a simple implicit scheme without approximate factorization and coefficient block-diagonal system of equations. This results in a significant improvement in computational efficiency as compared to the well-known Beam-Warming and Steger implicit factored schemes. This is because the present approach has the advantageous characteristics in the creation of higher order numerical implicit terms. The current method is spatially second-order accurate, fully conservative and implemented using general coordinate transformations for treating complex geometries. The scheme shows good convergence rate and accuracy in capturing the shock waves.