Publications Details

Conservative and Entropy-Stable Nonconformal Interfaces With Lower Accuracy Quadrature: Circumventing the Inner-Product Preservation Property

Crean, Jared C.; Fisher, Travis C.

The use of p-, and ℎp-nonconformal interfaces enables greater geometric flexibility in performing computational science simulations, especially when relying on efficient tensor-product-based high-order Summation-by-Parts element schemes. For high-speed compressible computational fluid dynamics, the underlying numerical method must be conservative such that the discretization of the governing equations satisfies the Rankine Hugoniot relations. This paper extends the conservative nonconformal interface method of [1] to Summation-by-Parts elements with face quadratures of degree less than 2p, specifically allowing which allows the use of tensor-product elements on the Legendre-Gauss-Lobatto nodes, which are accurate up to degree 2p − 1. This formulation does not satisfy the inner-product preservation property of [1], but nonetheless remains conservative, entropy stable, and free-stream preserving. Mathematical theory is developed to determine the required accuracy of the mortar grid quadrature rule, and numerical results verify the mathematical results.