An analysis of finite-difference and finite-volume formulations of conservation laws
Journal of Computational Physics
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
Journal of Computational Physics
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
Short Note: ADI-SGS scheme on ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Skew-symmetric convection form and secondary conservative finite difference methods for moving grids
Journal of Computational Physics
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The role of a geometric conservation law (GCL) on a finite-difference scheme is revisited for conservation laws, and the conservative forms of coordinate-transformation metrics are introduced in general dimensions. The sufficient condition of a linear high-order finite-difference scheme is arranged in detail, for which the discretized conservative coordinate-transformation metrics and Jacobian satisfy the GCL identities on three-dimensional moving and deforming grids. Subsequently, the geometric interpretation of the metrics and Jacobian discretized by a linear high-order finite-difference scheme is discussed, and only the symmetric conservative forms of the discretized metrics and Jacobian are shown to have the appropriate geometric structures. The symmetric and asymmetric conservative forms of the metrics and Jacobian are examined by the computation of an inviscid compressible fluid on highly-skewed stationary and deforming grids using sixth-order compact and fourth-order explicit central-difference schemes, respectively. The resolution of the isentropic vortex and the robustness of the computation are improved by employing symmetric conservative forms on the coordinate-transformation metrics and Jacobian that have an appropriate geometry background. An integrated conservation of conservative quantities is also attained on the deforming grid when symmetric conservative forms are adopted to the time metrics and Jacobian.