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

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.

High-Order Large-Eddy Simulations of a Ducted Wind Turbine

“…These restrictions are imposed for explanation purposes only and can be easily lifted in practice. More details can be found in our previous papers [25][26][27][28][29][30][31]34]. Since the SPs on the two sides of a nonconforming sliding interface do not match, we aim to find the best-possible common values of a variable on the two sides of a sliding interface.…”

“…Besides the flow equations, the Geometric Conservation Law(GCL) [35] also needs to be numerically satisfied to ensure free-stream preservation on moving grids. The GCL equations and the steps for solving them are described in [30,31,34]…”

“…These methods were later extended to sliding-deforming meshes [27] and to deal with 3D geometries [28]. Zhang et al [29][30][31] further introduced the transfinite mortar concept that has no geometric error and makes a sliding-mesh method arbitrarily high-order accurate in space and high-order in time. This method has been applied to simulate flows around rotating cylinders of different cross-sectional shapes [32], flapping wings for energy harvesting [33], and more recently the first high-order eddy-resolving simulation of flow over a marine propeller [34] This study employs the solver developed by Zhang et al to study the loads and flow fields of a wind turbine in a ducted and an open configurations.…”