Summary This paper describes the implementation of a numerical solver that is capable simulating compressible flows nonideal single‐phase fluids. The proposed method can be applied to arbitrary equations state and suitable for all Mach numbers. pressure‐based uses operator‐splitting technique based on PISO/SIMPLE algorithm: density, velocity, temperature fields are predicted by solving linearized versions balance using convective fluxes from previous iteration or time step. overall mass...

Vortex particle methods of computational hydrodynamics are widely employed by engineers to solve the problems flow simulation and estimation unsteady hydrodynamic loads acting on bodies. The main advantage such is a relatively low cost, but their applicability limited subsonic incompressible single-phase non-heat-conducting flows. If high order discretization required, usage direct algorithms leads significant increase in complexity memory demand. To overcome this limitation, approximate...

This article describes the open-source C++ code VM2D for simulation of two-dimensional viscous incompressible flows and solving fluid-structure interaction problems. The is based on Viscous Vortex Domains (VVD) method developed by Prof. G. Ya. Dynnikova, where viscosity influence taken into account introducing diffusive velocity. original VVD was supplemented author’s algorithms boundary condition satisfaction, which made it possible to increase accuracy flow near airfoil’s surface line...

The possibilities of applying the pure Lagrangian vortex methods computational fluid dynamics to viscous incompressible flow simulations are considered in relation various problem formulations. modification methods—the Viscous Vortex Domain method—is used which is implemented VM2D code developed by authors. Problems simulation around airfoils with different shapes at Reynolds numbers considered: Blasius problem, circular cylinders numbers, a wing airfoil 104 and 105, two closely spaced...

New numerical schemes are proposed for solving the boundary integral equation that arises in CFD vortex particle methods of when simulating a plane flow around smooth airfoils. They based on considering 2-nd kind with respect to sheet intensity bounded or absolutely integrable kernel instead traditionally solved singular equations 1-st Hilbert-type singularity. To solve it, Galerkin approach is used. It shown approximating airfoil polygon, it possible develop and order accuracy,...

We consider the methodology of numerical schemes development for two-dimensional vortex method. describe two different approaches to deriving integral equation unknown sheet intensity. simulate velocity surface line an airfoil as influence attached and source sheets. a polygonal approximation assume intensity distributions free sheets be approximated with piecewise constant or linear (continuous discontinuous) functions. several specific that provide accuracy have computational cost. The...

Abstract The problem of 2D incompressible flow simulation around airfoils using vortex methods is considered. An exact solution for the boundary integral equation with respect to a free sheet intensity at airfoil surface line that arises in such problems obtained. constructed flows elliptical and Zhukovsky theory complex potentials conformal mappings technique. It possible take into account influence singularities domain — point vortices which simulate wake. obtained solutions can be used...

A software package is developed for numerical simulation of wind turbine rotors autorotation by using the modified LS-STAG level-set/cut-cell immersed boundary method. The level-set function used boundaries description. Algorithm construction complex-shaped airfoils, based on Bézier curves usage, proposed. Also, algorithm recalculation at any time without reconstructing curve each new rotor position described. designed second-order Butterworth low-pass filter aerodynamic torque filtration...

Open Source C++ code is developed for 2D incompressible flow simulation by using vortex methods. The has modular structure, it permits users to simulate around airfoils (as well as system of airfoils) and compute unsteady hydrodynamic loads acting the airfoils. It also possible hydroelastic regimes airfoil motion in weakly coupled strongly algorithms. Well known methods algorithms original numerical schemes authors are implemented, which makes raise accuracy significantly comparison...

Two coupling strategies for numerical simulation in Fluid-Structure Interaction problems using vortex methods are considered and implemented new open-source code VM2D developed by the authors 2D incompressible flows simulations around airfoils methods. The first strategy called "partitioned approach" implies that hydrodynamical subproblem mechanical one solved separately, step-by-step. However, this method has limited range of applicability. In second "monolithic these two subproblems...

Галепова В. Д., Лукин В., Марчевский И. К., Фуфаев И

The problem of the accuracy improving is considered for vortex method. It shown, that airfoil surface line representation as a polygon consisting rectilinear panels can lead to incorrect behavior numerical solution boundary integral equation with respect unknown sheet intensity, especially in case considerably different lengths neighboring panels. approach developed which makes it possible take into account explicitly curvature line. approximate formulae coefficients linear system are...

The implementations of 2D vortex element method adapted to different types parallel computers are considered. developed MPI-implementation provides close linear acceleration for small number computational cores and approximately 40-times 80-cores cluster when solving model problem. OpenMP-based modification allows obtain 5% additional due shared memory usage. Approximate fast multipole usage reduces time computations significantly: 11 times the testmodel problem in sequential mode 3.5...

Abstract The algorithm of the Viscous Vortex Domain method implemented in author’s code VM2D is investigated. This allows simulating 2D viscous incompressible flows and solving fluid-structure interaction problems. verification algorithm, namely, correctness taking into account viscosity effect, performed on well-studied test problems flow simulation around a circular cylinder for Reynolds numbers range 20 . 200: problem impulse start considered, dependency separation angle number comparison...

Abstract The approximate fast algorithm is developed that makes it possible to calculate velocities of the vortex particles in two-dimensional flow simulations by using methods. It adapted efficient solution boundary integral equation arising at each time step simulation. proposed method can be considered as generalization classical Barnes – Hut method, taking into account some ideas Fast Multipole Method. Some model problems are solved methods, implemented for multi-cores CPUs and (with...

Significant part of the computational work in numerical simulations technical systems, physical phenomena and technological processes is solving linear algebraic equations systems arising from discretization corresponding differential or integrodifferential equations. There are several classes iterative methods for solving, which differ by approach to construction next approximation. These based on splitting, variational-type projection-type methods. The aim this study development efficiency...

A droplet impact on a deep pool can induce macro-scale or micro-scale effects like crown splash, high-speed jet, formation of secondary droplets thin liquid films, etc. It depends the diameter and velocity droplet, properties, external forces other factors that ratio dimensionless criteria account for. In present research, we considered consist same viscous incompressible liquid. We took surface tension into but neglected gravity forces. used two open-source codes (OpenFOAM Gerris) for our...