A Conservative High-Order Method Utilizing Dynamic Transfinite Mortar Elements for Flow Simulation on Curved Sliding Meshes

TL;DR

This paper introduces a high-order, conservative flow simulation method on curved sliding meshes using dynamic transfinite mortar elements, enabling accurate, stable, and efficient handling of complex rotating interfaces.

Contribution

It develops a novel high-order, conservative method with dynamic mortar elements for flow on curved sliding meshes, improving accuracy and stability over existing approaches.

Findings

Achieves arbitrarily high-order accuracy in space.

Ensures conservation and outflow conditions.

Effectively handles multiple rotating objects.

Abstract

We present a high-order method for flow simulation on unstructured curved nonconforming sliding meshes. This method utilizes dynamic transfinite mortar elements to exchange flow information between the two sides of a sliding interface. The method is arbitrarily high-order accurate in space, provably conservative, and satisfies outflow condition. Moreover, it retains the accuracy of a time marching scheme, and thus allows substantial reduction of rotational speed effects when equipped with a high-order temporal scheme. The method's capability of simultaneously handling multiple rotational objects is also explored. Details on the implementation are provided as well.