| Popis: |
An implicit finite volume algorithm is developed for higher-order unstructured computation of inviscid compressible flows. The Spectral Finite Volume method is used to achieve high-order spatial discretization of the domain, coupled with a matrix-free LU-SGS algorithm to solve the linear systems arising from implicit time marching of the governing equations, avoiding the explicit storage of the flux Jacobian matrices. A new limiter formulation for the high-order terms of the reconstruction polynomial is introduced. The issue of mesh refinement in accuracy measurements for unstructured meshes is investigated. A straightforward methodology is applied for accuracy assessment of the higher-order unstructured approach based on entropy levels and direct solution error calculation. The accuracy, fast convergence and robustness of the proposed higher-order unstructured solver for different speed regimes are demonstrated via several known test cases from the literature for the 2nd-, 3rd- and 4th-order discretizations. The possibility of reducing the computational cost required for a given level of accuracy using high-order discretization is demonstrated. The main features of the present methodology include the reconstruction algorithm that yields 2nd-, 3rd- and 4th-order spatially accurate schemes, an implicit time march algorithm, high-order domain boundaries representation and a hierarchical moment limiter to treat flow solution discontinuities. |
