Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation

For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR&WENO is accurate and have a high resolution. Moreover, we evaluate and compare the performance between the uniform mesh WENO scheme and the parallel AMR&WENO The research of the first two authors is supported by the National Natural Science Foundation of China under grants 11325208 and 11221202, and the Foundation of State Key Laboratory of Explosion Science and Technology (Grant No. ZDKT11-01). The research of the third author is supported by AFOSR grant F49550-12-1-0399 and NSF grant DMS-1418750. ∗Corresponding author: [email protected] Preprint submitted to Elsevier March 19, 2015 method. The comparison results provide us further insight into the high performance of the parallel AMR&WENO method.