A High Order Finite Volume Method for 3D Elastic Modelling on Unstructured Meshes
In this chapter, a new efficient high order finite volume method for 3D elastic modelling on unstructured meshes is developed. The stencil for the high order polynomial reconstruction is generated by subdividing the relative coarse tetrahedrons. The reconstruction on the stencil is performed by using cell averaged quantities represented by the hierarchical orthonormal basis functions. Unlike the traditional high order finite volume method, the new method has a very local property like the discontinuous Galerkin method. Furthermore, it can be written as an inner split computational scheme which is beneficial to reducing computational amount. The reconstruction matrix is invertible and remains unchanged for all tetrahedrons, and thus it can be pre computed and stored before time evolution. These special advantages facilitate the parallelization and high order computations. The high order accuracy in time is obtained by the Runge Kutta method. Numerical computations including a 3D real model with complex topography demonstrate the effectiveness and good adaptability to complex topography.