The article presents numerical modeling of meteorological processes in the wind farm of the Republic of Adygea. The wind farm has 60 wind turbines, the capacity of each wind turbine is 2.5 MW. A test configuration wit...
The article presents numerical modeling of meteorological processes in the wind farm of the Republic of Adygea. The wind farm has 60 wind turbines, the capacity of each wind turbine is 2.5 MW. A test configuration with 4 nested domains was developed to study the wind farm. The computations were carried out using the WRF-ARW computational code with the wind turbine parameterization module. The calculation was performed for the period 01.04.2020 00:00 – 01.05.2020 00:00 UTC. As a result, the dimensions of the wake formed by the wind farm were obtained, and the influence of the parameterization of wind turbines on the wind distribution calculation was shown. The potential vortex wake can reach sizes up to 15 km. The losses of generated power can reach 1 MW inside the vortex wake. The computations were run on high performance cluster UNIHUB of ISP ras.
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 vortex sheet intensity at the airfoil su...
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 vortex sheet intensity at the airfoil surface line that arises in such problems is obtained. The exact solution is constructed for flows around elliptical and Zhukovsky airfoils using the theory of complex potentials and conformal mappings technique. It is possible to take into account the influence of singularities in the flow domain — point vortices which simulate vortex wake. The obtained exact solutions can be used to verify and estimate the accuracy of numerical schemes for the boundary integral equation solution: such procedure is also described in details.
The problem of the flow simulation around airfoils using Lagrangian vortex methods is considered. Numerical schemes of the second order of accuracy for free vortex sheet intensity distribution along the airfoil are de...
The problem of the flow simulation around airfoils using Lagrangian vortex methods is considered. Numerical schemes of the second order of accuracy for free vortex sheet intensity distribution along the airfoil are developed for smooth and non-smooth airfoils. The schemes are based on the Galerkin approach with piecewise-constant and piecewise-linear basis functions. The finite element method ideas are used and the resulting piecewise-linear scheme has the same numerical complexity as the scheme with piecewise-constant numerical solution. The modification of a FEM-type scheme is developed for non-smooth airfoils which permits to take into account the discontinuity of the solution at the specified points; its computational cost increases insignificantly.
One of the efficient ways to speedup calculations in the vortex method, namely the Barnes – Hut-type algorithm, is considered. This method is based on the introducing of a hierarchical structure of domains (binary tr...
One of the efficient ways to speedup calculations in the vortex method, namely the Barnes – Hut-type algorithm, is considered. This method is based on the introducing of a hierarchical structure of domains (binary tree), which allows one to take into account approximately mutual influences of clusters of vortex elements located far from each other when calculating convective velocities. Estimates of the computational complexity of the algorithm for convective velocities calculating are derived, as well as estimates of the error, which depend on the parameters of the algorithm. In practice, these estimates make it possible to choose optimal values of the algorithm parameters and to achieve the maximal speedup of calculations at a given level of acceptable calculation error.
This paper is devoted to a numerical simulation of 2D gas dynamics flows on uniform rectangular meshes using the Runge - Kutta - Discontinuous - Galerkin (RKDG) method. The RKDG algorithm was implemented with in-house...
This paper is devoted to a numerical simulation of 2D gas dynamics flows on uniform rectangular meshes using the Runge - Kutta - Discontinuous - Galerkin (RKDG) method. The RKDG algorithm was implemented with in-house C++ code based on the experience in the investigation of 1D case. The advantage of the RKDG method over the most popular finite volume method (FVM) is discussed: three basis functions being applied in the framework of the RKDG approach lead to a considerable decrease of the numerical dissipation rate with respect to FVM. The results of the acoustic pulse simulation on a sufficiently coarse mesh with the piecewise-linear approximation show a good agreement with the analytical solution in contrast to the FVM numerical solution. For the Sod problem, the results of the discontinuities propagation illustrate the dependence of the scheme resolution on the numerical fluxes, troubled cell indicator and the limitation technique choice. The possibility to resolve strong shocks is demonstrated with the Sedov cylindrical explosion test.
A novel algorithm of the Lagrangian vortex method is considered for incompressible flow simulation. The boundary condition on the body surface is satisfied by vortex sheet introduction, which intensity is determined f...
A novel algorithm of the Lagrangian vortex method is considered for incompressible flow simulation. The boundary condition on the body surface is satisfied by vortex sheet introduction, which intensity is determined from the equality between the tangential components of flow velocity limit value and the body surface velocity. High accuracy of velocity field reconstruction in the neighbourhood of the body surface permits to estimate unsteady aerodynamic loads for the complex-shaped bodies, including added masses tensor components with rather low computational cost.
This paper is devoted to the simulation of the two-dimensional gas flows with oscillations and discontinuities using the Runge — Kutta Discontinuous Galerkin (RKDG) method, that has been implemented in the code proto...
This paper is devoted to the simulation of the two-dimensional gas flows with oscillations and discontinuities using the Runge — Kutta Discontinuous Galerkin (RKDG) method, that has been implemented in the code prototype written in C++. It implements the HLLC numerical flux, the KXRCF troubled cells indicator, the WENO S limiter with the local characteristic decomposition approach and algorithm of dynamic time step control. The computations could be performed on unstructured meshes with mixed cell types (quadrangular and triangular) which can be built in any mesh bulder in IDEAS UNV format (i.e. SALOME). The code is verified on the common numerical tests such as pulsating and vibrating cylinders, Sod-like cylindrical explosion, forward-facing step, blast wave problem. Comparison between analytical solution and numerical results obtained with the in-house code and the open-source OpenFOAM package is presented.
The LS-STAG immersed boundary cut-cell method modification for viscoelastic flow computations is presented. Rate type viscoelastic flow models (linear and quasilinear) are considered. Rate type viscoelastic flow model...
The LS-STAG immersed boundary cut-cell method modification for viscoelastic flow computations is presented. Rate type viscoelastic flow models (linear and quasilinear) are considered. Rate type viscoelastic flow models (linear and quasilinear) are considered. The obtained numerical method is implemented in the LS-STAG software package developed by the author. This software allows to simulate viscous incompressible flows by using the LS-STAG method and it modifications. The LS-STAG-discretization of extra-stress equations for viscoelastic Maxwell, Jeffreys, upper-convected Maxwell, Maxwell-A, Oldroyd-B, Oldroyd-A, Johnson Segalman fluids was developed. Formulae for differential types of convected time derivatives (Oldroyd, Cotter — Rivlin, Jaumann — Zaremba — Noll derivatives) the LS-STAG discretization was obtained. Normal non-newtonian stresses are computed at the centers of base LS-STAG mesh cells and shear non-newtonian stresses are computed at the cell corners. Time-stepping algorithm is based on the first order predictor-corrector scheme. To validate developed numerical method the test problem about viscoelastic Oldroyd-B flow past a circular airfoil was used. Computational experiments were carried out at Weissenberg number in the range from 0 to 4. The computed values of the drag coefficients and the wake length are in good agreement with the experimental data.
The results of comparative study of the WENO-type monotonization methods for numerical solution of the Euler equations computed by the discontinuous Galerkin method are presented. The variants of the technique based o...
The results of comparative study of the WENO-type monotonization methods for numerical solution of the Euler equations computed by the discontinuous Galerkin method are presented. The variants of the technique based on Lagrangian and Hermitian interpolation are analyzed. Test simulations for the Sod problem, which solution contains a shock wave, a rarefaction wave, and a contact discontinuity, are performed. The merits and demerits of the considered variants of the limiters including the questions of the numerical solution monotonicity, numerical dissipation magnitude, computational costs and extensibility of software implementation are investigated.
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