Wavelet-based adaptive multi-resolution solver on heterogeneous parallel architecture for computational fluid dynamics

Abstract

For the efficient simulation of fluid flows governed by a wide range of scales a wavelet-based adaptive multi-resolution solver on heterogeneous parallel architectures is proposed for computational fluid dynamics. Both data-and task-based parallelisms are used for multicore and multi-GPU architectures to optimize the efficiency of a high-order wavelet-based multi-resolution adaptative scheme with a 6th-order adaptive central-upwind weighted essentially non-oscillatory scheme for discretization of the governing equations. A modified grid-block data structure and a new boundary reconstruction method are introduced. A new approach for detecting small scales without using buffer levels is introduced to obtain additional speed-up by minimizing the number of required blocks. Validation simulations are performed for a double-Mach reflection with different refinement criteria. The simulations demonstrate accuracy and computational performance of the solver.

Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure

“…Cohen et al [9], Han et al [21]). Multi-phase flows have been recently addressed with smooth-interface models (Hejazialhosseini et al [20], Rossinelli et al [22]).…”

“…In most Refs. [9,10,18,19,21] the differences (called details) at a level l + 1 were described as prediction errors between exact values at level l + 1 and predicted values from level l. For this purpose, first, exact cell-averages at the level l were calculated from the ones of level l + 1 by using a projection operator P l+1→l (Fig. 1, left).…”

“…However, unlike their choice of non-overlapping blocks (tiles in [27]) as the basic parallel units, we use partially overlapping ones to obtain better parallelism. For remedying limited memory efficiency of approaches in [6,21], our present data structure adopts storage-and-operation-splitting techniques to separate a block from its associated computational cell data. Relative to blocks, cells are finer-grained into data packages and stored in a memory pool [28].…”

“…To make sure that high-order interpolation schemes can be employed for flux computations at the block boundaries where the grid resolution varies, auxiliary boundary cell data are temporarily reconstructed during each evolution. To avoid the temporary memory allocation and deallocation in every block at each time step, in [21] memory was permanently allocated to store boundary cell data for all grid blocks, which finally increased the parallelism to an ever higher level with the help of a multi-step boundary rebuilding approach. However, partially overlapping blocks result in a severe memory inefficiency, especially for three dimensional simulations.…”

“…Relative to blocks, cells are finer-grained into data packages and stored in a memory pool [28]. Since packages do not overlap with each other, there is no extra memory required for the data associated with overlapping regions among adjacent blocks, and inter-block communications [21] are achieved implicitly by shared memory. To be able to track the interface as accurately as possible, we update the adaptive data structure first by the actual interface position to ensure all near-interface regions required by the sharp-interface model are refined to the finest grid level.…”