A high-order flux reconstruction method with adaptive mesh refinement and artificial diffusivity on unstructured moving/deforming mesh for shock capturing

- A high-order method of shock-capturing on unstructured dynamic grids is proposed.
- The robust and efficient AMR features direct addressing and compact memory layout.
- A physically consistent artificial diffusivity removes the Gibbs oscillation.
- High-order accuracy is obtained under complex grid motion and adaptation.
- The FR-AMR-AD framework can stabilize and capture various sharp shock solutions.

This article presents new progress of shock capturing on unstructured dynamic grids by using adaptive mesh refinement (AMR) method in conjunction with artificial diffusivity (AD) under the framework of flux reconstruction (FR)/correction procedure via reconstruction (CPR) method. The proposed AMR algorithm is applicable even when the grid undergoes dynamic motion. It features an innovative data structure that is capable of direct addressing in managing the system of cells on multiple levels of refinement. A conservative mortar method is used to handle non-conforming interfaces resulted from cell subdivision. The AD is added in regions of strong dilatation to counter the Gibbs oscillation that is disruptive to high-order solutions when shock discontinuities exist. Several test cases are used to verify that this FR-AMR-AD framework can achieve high-order accuracy for smooth flows, and obtain stable solution with the presence of shock discontinuity. By further limiting the shock within subdivided adjacent cells, a sharp shock solution can be obtained with reduced amount of AD addition, hence errors from adding dissipation, on dynamically refined grids.