Efficient Convergence for a Higher-Order Unstructured Finite Volume Solver for Compressible Flows

This Paper presents a three-dimensional higher-order-accurate finite volume algorithm for the solution of steady-state compressible flow problems. Higher-order accuracy is achieved by constructing a piecewise continuous representation of the average solution values using the k-exact reconstruction scheme. The pseudo-transient continuation method is employed to reduce the solution of the discretized system of nonlinear equations into the solution of a series of linear systems, which are subsequently solved using the generalized minimal residual (GMRES) method. This Paper considers several preconditioning methods in conjunction with different matrix reordering algorithms and shows that the proposed preconditioner based on inner GMRES iterations can enhance the convergence speed and reduce the memory cost of the solver. Moreover, when starting from a lower-order solution as the initial condition, this Paper shows that ramping up the Courant-Friedrichs-Lewy (CFL) number accelerates the convergence rate. Finally, this Paper verifies the developed finite volume algorithm by solving a set of test problems, in which optimal solution convergence with mesh refinement is attained.