ADER-DG with a-posteriori finite-volume limiting to simulate tsunamis in a parallel adaptive mesh refinement framework

A GPU implementation of adaptive mesh refinement to simulate tsunamis generated by landslides

ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement

We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resul...

Adaptive Mesh Refinement for Finite-volume Discretizations with Scalene Triangles

In this work, simulations with scalene triangle meshes represented by a recently proposed graphbased 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 ...

A mesh generation procedure to simulate bimaterials

It is difficult to develop an algorithm which is able to generate the appropriate mesh around the interfaces in bimaterials. In this study, a corresponding algorithm is proposed for this class of unified structures made from different materials with arbitrary shapes. The non-uniform mesh is generated adaptively based on advancing front technique available in Abaqus software. Implementing severa...

A Posteriori Error Estimate and Adaptive Mesh Refinement for the Cell-Centered Finite Volume Method for Elliptic Boundary Value Problems

We extend a result of Nicaise [13] for the a posteriori error estimation of the cell-centered finite volume method for the numerical solution of elliptic problems. Having computed the piecewise constant finite volume solution uh, we compute a Morley-type interpolant Iuh. For the exact solution u, the energy error ‖∇T (u− Iuh)‖L2 can be controlled efficiently and reliably by a residual-based a p...