A sweeping algorithm of unstructured elements in discontinuous spectral element method for thermal radiation in irregular multidimensional geometries

Abstract

The discontinuous spectral element method (DSEM) coupled with an element-by-element sweeping strategy is proposed as a solution to the radiative transfer equation (RTE) for participating media in irregular geometries. In the solving processing, a spatial domain of RTE is discretized by unstructured meshes; an angular direction of RTE is discretized as a set of contrast angles by structured quadrilateral meshes. Then, both spatial domain and angular direction are coupling solved by DSEM. However, this coupling solution leads to a large-scale matrix problem. To address this, the element-by-element sweeping strategy optimizes the ordering of unstructured spatial elements. Several examples are provided to demonstrate the effectiveness of DSEM with the element-by-element sweeping strategy. Compared to the original sweep strategy, the element-by-element approach significantly improves calculation efficiency and reduces computational time.

Keywords

• Element-by-element sweeping strategy
• Discontinuous spectral element method
• Thermal radiation
• Irregular geometry
• Calculation efficiency