Extending the Building Cube Method to Curvilinear Mesh with Adaptive Mesh Refinement

Abstract

Building Cube Method (BCM) adopts block-structured Cartesian mesh and finer resolution can be used where the flow contains detailed flow structures. This paper reports the recent progress in extending BCM to curvilinear body-fitted mesh with Adaptive Mesh Refinement (AMR). Compared to Cartesian mesh based AMR, body-fitted AMR strategy is more complicated and less studied. In this paper the key components of body-fitted curvilinear mesh based AMR are introduced. A pressure based refinement criterion is used to detect both shock wave and strong vortex. Cubic interpolation is used to preserve the quality of the refined mesh. A sub-block based refinement strategy is also developed for the treatment of singular geometry features. Combined with the high order scheme, an accurate and robust curvilinear mesh based AMR tool is developed with which the flow details can be automatically captured. Numerical examples are given to validate the numerical properties of current AMR tool and to demonstrate the benefits of current body-fitted AMR strategy.