GPU-РЕАЛІЗАЦІЯ РОЗРАХУНКУ ПРАВОЇ ЧАСТИНИ СЛАР У МЕТОДІ ДИСКРЕТНИХ ВИХРОВИХ РАМОК ДЛЯ ЗАДАЧ ОБТІКАННЯ ТОНКИХ ПЛАСТИН

This work explores the use of a graphics processing unit (GPU) to compute the right-hand side of a system of linear algebraic equations (SLAE) within the discrete vortex method when modeling the flow around thin flat plates in an ideal fluid. In addition, the velocity of the vortex sheet nodes was also computed on the GPU. The algorithm for GPU-based computation was implemented using the GLSL programming language for compute shaders, supported in the OpenGL standard starting from version 4.3. For CPU-based calculations, the C# programming language and the OpenTK framework were used. Parallelization on the CPU was achieved using the static method Parallel. For. The CPU implementation operates with double-precision numbers, while the GPU implementation uses single-precision arithmetic and avoids conditional operators to improve performance. A comparative analysis of the accuracy and performance was carried out for flow simulations around plates of different sizes and angles of attack. The results of numerical experiments demonstrate that, with a loss in accuracy of less than 1 % (in terms of pressure distribution and total force), a significant speedup of up to 75 times can be achieved, depending on the number of vortex elements. A noticeable increase in error is observed as the simulation time in-creases tmax = 6 ; however, at that point, the method may become physically invalid due to self-intersection of the vortex sheet. It was found that transferring only the right-hand side SLAE computation to the GPU yields a 10× speedup of the overall calculation. The obtained results confirm the feasibility and effectiveness of offloading the right-hand side computation to the GPU for simulating three-dimensional plate flows using the discrete vortex method.