The VM2D Open Source Code for Two-Dimensional Incompressible Flow Simulation by Using Fully Lagrangian Vortex Particle Methods

Abstract

This article describes the open-source C++ code VM2D for the simulation of two-dimensional viscous incompressible flows and solving fluid-structure interaction problems. The code is based on the Viscous Vortex Domains (VVD) method developed by Prof. G. Ya. Dynnikova, where the viscosity influence is taken into account by introducing the diffusive velocity. The original VVD method was supplemented by the author’s algorithms for boundary condition satisfaction, which made it possible to increase the accuracy of flow simulation near the airfoil’s surface line and reduce oscillations when calculating hydrodynamic loads. This paper is aimed primarily at assessing the efficiency of the parallelization of the algorithm. OpenMP, MPI, and Nvidia CUDA parallel programming technologies are used in VM2D, which allow performing simulations on computer systems of various architectures, including those equipped with graphics accelerators. Since the VVD method belongs to the particle methods, the efficiency of parallelization with the usage of graphics accelerators turns out to be quite high. It is shown that in a real simulation, one graphics card can replace about 80 nodes, each of which is equipped with 28 CPU cores. The source code of VM2D is available on GitHub under GNU GPL license.

Hybrid Barnes – Hut/Multipole algorithm application to vortex particles velocities calculation and integral equation solution

“…The structure and options of the VM2D code are briefly described in [9]. However, the development of the VM2D continues, some other features are available in recent versions, as well as improved algorithms for essential operations.…”

On open third-party libraries usage in implementation of vortex particle methods of computational fluid dynamics

“…Marshal (США) и другими. Коллективом авторов [20,21] разработан пакет VM2D, свободно доступный по ссылке https://github.com/vortexmethods/VM2D с исходным кодом на языке C++. Он предназначен для решения широкого круга плоских задач, в том числе в сопряженной гидроупругой постановке.…”

Singularity resolving in solution of the boundary integral equation in two-dimensional vortex methods

“…At the same time, the results of the accuracy investigation of known numerical schemes (that can be applied in 2D problems being solved by vortex particle methods) performed for model problems with known exact solution [5], show that the error can be high enough, and it can be the most significant factor that bounds the accuracy of the flow simulation. A more detailed review of the problems being solved, as well as the VM2D code developed directly by the authors which allows simulating twodimensional incompressible flows around movable and immovable airfoils, is presented in [6]. In the present paper, the original approach is suggested that allows for improving the accuracy of the BIE solution for airfoils with sharp edges or corner points where the exact solution has the singularity.…”