Adaptive Mesh Refinement for Finite-volume Discretizations with Scalene Triangles

In this work, simulations with scalene triangle meshes represented by a recently proposed graph-based adaptive mesh refinement technique are described. Previously, simulations exclusively with isosceles right triangles were presented with this graph-based scheme. This data structure represents triangular meshes in finite-volume discretizations in order to solve second-order partial differential equations. The main advantages of using this graph-based adaptive triangular mesh refinement technique are that low computational cost to adapt and traverse the mesh and low computational storage cost are achieved. This paper is a result of a work in modeling the Laplace equation with scalene triangles.