An Adaptive Visualization Tool for High Order Discontinuous Galerkin Method with Quadratic Elements

Abstract

High order discretization method is one of the most popular research topics on Computational Fluid Dynamics (CFD). However, the development of visualization tools suited for high order methods obtains not as much attention. Most of the software used to visualize numerical solutions do not support high order data format. To visualize the high order solution, the most common method is to tessellate the solution with linear subdivision and then generate the values by resampling. This paper describes an efficient approach for Discontinuous Galerkin Method (DGM) based on OpenFOAM and VTK. We design a method to estimate the visualization error and introduce gaussian quadrature method to calculate it. Under the limit of visualization error set by user, the high order DGM solution is tessellated into a set of quadratic elements and converted into VTK data. By implementing the interpolation interface, this tools can support other discretization methods. The tool is tested with a series of cases. Accurately visualization of geometric information and field attributes are obtained. Comparing to linear methods, less computation and space cost are needed to reach the same visualization error limit.