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Despite the continuous improvement of technology, generation of high-quality meshes around complicated geometry remains a time consuming and even laborious task. In this paper, we propose a semi-meshless computational framework designed to reduce the difficulty in generating the necessary point connectivity for numerically solving conservation laws. The new framework is based on an analytic formulation of conservation laws in a generalized coordinate frame, in which the time derivatives of the conservative variables can be computed using a weighted average of estimates from local stencils. This formulation naturally implies a merit function for generating stencils based on point distances and the orthogonality of the generalized coordinates in the expected stencils. We applied the framework to solving the Euler equations for inviscid flow. Test cases involving airfoils showed that the new computational framework produced numerical solutions with quality similar to their finite volume counterparts.

An Edge-Averaged Semi-Meshless Framework for Numerical Solution of Conservation Laws