Mesh–Order Independence in CFD Simulation

Accuracy and performance are key issues for CFD simulation. How to meet the specific accuracy requirements, as well as the optimal simulation performance, is always the research hotspot. This paper presents a general theory of Mesh-Order Independence that is used to guide the configuration of two of the most critical control parameters in a concrete CFD simulation process: grid spacing and discretization order. A concept of optimal mesh-order independent pair which can meet both accuracy and performance requirements at the same time is proposed and analyzed. To find the optimal Mesh-order independent pair, the Mesh-Order Independence is applied to high order FEM simulation, and the specific process and key technologies are detailed. Test and results of two benchmark cases, the Laplace equation and the Helmholtz equation, show that the Mesh-order theory proposed in this paper provides an important guidance for the grid spacing selection and discretization order configuration in practical simulation, especially in the case of high precision requirements. Specifically, only 6 pre-runs with low discretization orders and coarse meshes are needed for the both cases to have a prediction accuracy of more than 70%.