A parallel modular computing environment for three-dimensional multiresolution simulations of compressible flows

Numerical investigation of compressible flows faces two main challenges. In order to accurately describe the flow characteristics, high-resolution nonlinear numerical schemes are needed to capture discontinuities and resolve wide convective, acoustic and interfacial scale ranges. The simulation of realistic three-dimensional (3D) problems with state-of-the-art finite-volume method (FVM) based on approximate Riemann solvers with weighted nonlinear reconstruction schemes requires the usage of high-performance computing (HPC) architectures. Efficient compression algorithms reduce computational and memory load. Fully adaptive multiresolution (MR) algorithms with LTS have proven their potential for such applications. While modern central processing units (CPUs) requires multiple levels of parallelism to achieve peak performance, the fine-grained MR mesh adaptivity results in challenging compute/communication patterns. Moreover, local time stepping (LTS) incurs strong data dependencies which challenge a parallelization strategy. We address these challenges with a block-based MR algorithm, where arbitrary cuts in the underlying octree are possible. This allows for a parallelization on distributed-memory machines via the Message Passing Interface (MPI). We obtain neighbor relations by a simple bit-logic in a modified Morton Order. The block-based concept allows for a modular setup of the source code framework in which the building blocks of the algorithm, such as the choice of the Riemann solver or the reconstruction stencil, are interchangeable without loss of parallel performance. We present the capabilities of the modular framework with a range of test cases and scaling analysis with effective resolutions beyond one billion cells using O(10⁴) cores.