87 / 2019-09-30 22:50:33

Multiderivative Combined Dissipative Compact Scheme Satisfying Geometric Conservation Law

Multiderivative combined dissipative compact scheme, multiderivative formulation, dissipative interpolation, geometric conservation law, complex geometry

In order to improve the resolution power of the hybrid cell-edge and cellnode dissipative compact schemes (HDCS), a series of multiderivative combined dissipative compact schemes (MDCS) have been proposed in this paper. The design concept of the HDCS has been followed to develop the MDCS satisfying the geometric
conservation law (GCL) and possessing inherent dissipation. Evaluations of multiple
derivatives are included in the MDCS for the purpose of increasing the scheme resolution. The performance of the MDCS is evaluated by theoretical analysis and numerical
tests. The multiple derivatives demonstrate their capability in significantly improving
resolution power of the MDCS. A MDCS can achieve much higher resolution power
than a HDCS with the same order of accuracy. Based on the solutions of the transition
and turbulence decay in three-dimensional Taylor-Green vortex, a fifth-order MDCS
with three tri-diagonal operators is recommended. This MDCS has better performance
than the fifth-order HDCS in resolving multiple-scales turbulent structures.