Parallelization of numerical solutions of shallow water equations by the finite volume method for implementation on multiprocessor systems and graphics processors

• Main Author: Сорокін, М.В.
• Format: Article
• Language: Ukrainian
• Published: Kyiv National University of Construction and Architecture 2023
• Subjects: моделювання річкових систем; моделювання прибережних зон моря; рівняння мілкої води; скінченні об’єми; неструктуровані сітки; паралельні обчислення; обчислення на GPU; MPI; OpenACC; river modeling; coastal modeling; shallow water equations; finite volume; unstructured grid; parallel computing; GPU computing
• Online Access: https://es-journal.in.ua/article/view/285081

An overview of approaches to parallelization of grid-based numerical methods for solving shallow water equations for multiprocessor systems and graphics processors is presented. A multithreaded approach for shared-memory computing systems implemented on the basis of the OpenMP programming interface and a geometric decomposition approach with message-passing using the MPI library for distributed-memory computers are described. Multithreading for programming GPUs based on the OpenACC software interface is considered. For the COASTOX-UN system of two-dimensional modeling of hydrodynamics, sediment and radionuclide transport in river systems and coastal areas of the seas, the parallelization of its hydrodynamic model COASTOX-HD was carried out. In the developed numerical model, the shallow water equations are solved by finite-volume numerical methods on unstructured computational grids with triangular cells of variable size. The parallelization is implemented using a hybrid MPI+OpenACC approach targeting multiprocessor systems and GPUs. For multiprocessor computers, geometric decomposition and MPI-based messaging are used, and for GPUs, multithreading is implemented using OpenACC directives. The performance of the developed parallel hydrodynamic model was evaluated during the calculation of typical problems of hydrodynamics of shallow water bodies, river flood, and tsunami wave run-up on the coast on a Dell Precision Workstation 7920 multi-core workstation with two 20-core Intel Xeon Gold 6230 processors and NVIDIA Quadro RTX 5000 and NVIDIA GeForce RTX 3080 graphics cards. It is shown that the developed model has significantly accelerated the simulation on the considered multiprocessor system and the considered GPUs. The acceleration on GPUs depends on the size of the computational grid, increasing to saturation with an increase in the number of grid cells. It is established that for the developed parallel model, whose numerical schemes are related to algorithms with low computational intensity, the memory bandwidth of the NVIDIA architecture GPUs is a more important limiting factor of acceleration than their performance.