摘要 :
Computation of viscous fluid flow is an area of research where many authors have tried to present different numerical methods for solution of the Navier-Stokes equations. Each of these methods has its own advantages and weaknesses...
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Computation of viscous fluid flow is an area of research where many authors have tried to present different numerical methods for solution of the Navier-Stokes equations. Each of these methods has its own advantages and weaknesses. In the meantime, many researchers have attempted to develop coupled numerical algorithms in order to save storage for computational purposes and to save computational time. In this paper, a new coupled method is presented for the first time by combining FDM and DRBEM for solving the stream function-vorticity formulation of the Navier-Stokes equations. The vorticity transport equation is analyzed using a finite difference technique while the stream function Poisson's equation is solved using a dual reciprocity boundary element method. Finally, the robustness and accuracy of the coupled FDM-DRBEM model is proved using the benchmark problem of the flow in a driven square cavity.
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We deal in this work with the Stokes equations set in a three-dimensional axisymmetric bounded domain. The boundary conditions that we consider are given on the normal component of the velocity and the tangential components of the...
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We deal in this work with the Stokes equations set in a three-dimensional axisymmetric bounded domain. The boundary conditions that we consider are given on the normal component of the velocity and the tangential components of the vorticity. Under assumptions on the data of the problem, the three-dimensional problem is reduced to a two-dimensional one. We write a stream function-vorticity formulation for this problem with two scalar unknowns. For the discretization, we use a domain decomposition method: the spectral element method which is well-adapted here. We prove the well-posedness of the obtained formulations and we derive error estimates between the exact solution and the discrete one.
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This paper describes the general convection-diffusion equation in 2D domain based on a particular fourth order finite difference method. The current fourth-order compact formulation is implemented for the first time, which offers ...
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This paper describes the general convection-diffusion equation in 2D domain based on a particular fourth order finite difference method. The current fourth-order compact formulation is implemented for the first time, which offers a semi-explicit method of solution for the resulting equations. A nine point finite difference scheme with uniform grid spacing is also put into action for discretization purpose. The proposed numerical model is based on the Navier-Stokes equations in a stream function-vorticity formulation. The fast convergence characteristic can be mentioned as an advantage of this scheme. It combines the enhanced Fournie's fourth order scheme and the expanded fourth order boundary conditions, while offering a semi-explicit formulation. To accomplish this, some coefficients which do not influence the solutions are also omitted from Fournie's formulation. Consequently, very accurate results can be acquired with a relatively coarse mesh in a short time. The robustness and accuracy of the proposed scheme is proved using the benchmark problems of flow in a driven square cavity at medium and relatively high Reynolds numbers, flow over a backward-facing step, and flow in an L-shaped cavity.
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A fourth-order compact finite difference scheme on the nine-point 2D stencil is formulated for solving the steady-state Navier-Stokes/Boussinesq equations for two-dimensional, incompressible fluid flow and heat transfer using the ...
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A fourth-order compact finite difference scheme on the nine-point 2D stencil is formulated for solving the steady-state Navier-Stokes/Boussinesq equations for two-dimensional, incompressible fluid flow and heat transfer using the stream function-vorticity formulation. The main feature of the new fourth-order compact scheme is that it allows point-successive overrelaxation (SOR) or point-successive under-relaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature.
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In this paper, we propose a high order characteristics tracing scheme for the two-dimensional nonlinear incompressible Euler system in vorticity stream function formulation and the guiding center Vlasov model. Such a scheme is inc...
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In this paper, we propose a high order characteristics tracing scheme for the two-dimensional nonlinear incompressible Euler system in vorticity stream function formulation and the guiding center Vlasov model. Such a scheme is incorporated into a semi-Lagrangian finite difference WENO framework for simulating the aforementioned model equations. This is an extension of our earlier work on high order characteristics tracing scheme for the 1D nonlinear Vlasov-Poisson system (Qiu and Russo in J Sci Comput 71:414-434, 2017). The effectiveness of the proposed scheme is demonstrated numerically by an extensive set of test cases.
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In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for stea...
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In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33-53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.
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This paper is devoted to the numerical analysis of a family of finite element approximations for the axisymmetric, meridian Brinkman equations written in terms of the stream-function and vorticity. A mixed formulation is introduce...
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This paper is devoted to the numerical analysis of a family of finite element approximations for the axisymmetric, meridian Brinkman equations written in terms of the stream-function and vorticity. A mixed formulation is introduced involving appropriate weighted Sobolev spaces, where well-posedness is derived by means of the Babuka-Brezzi theory. We introduce a suitable Galerkin discretization based on continuous piecewise polynomials of degree for all the unknowns, where its solvability is established using the same framework as the continuous problem. Optimal a priori error estimates are derived, which are robust with respect to the fluid viscosity, and valid also in the pure Darcy limit. A few numerical examples are presented to illustrate the convergence and performance of the proposed schemes.
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We develop an efficient fourth-order finite difference method for solving the incompressible Navier Stokes equations in the vorticity-stream function formulation on a disk. We use the fourth-order Runge-Kutta method for the time i...
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We develop an efficient fourth-order finite difference method for solving the incompressible Navier Stokes equations in the vorticity-stream function formulation on a disk. We use the fourth-order Runge-Kutta method for the time integration and treat both the convection and diffusion terms explicitly. Using a uniform grid with shifting a half mesh away from the origin, we avoid placing the grid point directly at the origin; thus, no pole approximation is needed. Besides, on such grid, a fourth-order fast direct method is used to solve the Poisson equation of the stream function. By Fourier filtering the vorticity in the azimuthal direction at each time stage, we are able to increase the time step to a reasonable size. The numerical results of the accuracy test and the simulation of a vortex dipole colliding with circular wall are presented.
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The paper deals with the multidomain Boundary Element Method (BEM) for modelling 2D complex turbulent flow using low Reynolds two equation turbulence models. While the BEM is widely accepted for laminar flow this is the first case...
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The paper deals with the multidomain Boundary Element Method (BEM) for modelling 2D complex turbulent flow using low Reynolds two equation turbulence models. While the BEM is widely accepted for laminar flow this is the first case, where this method is applied for a complex flow problems using k-ε turbulence model. The integral boundary domain equations are discretised using mixed boundary elements and a multidomain method also known as subdomain technique. The resulting system matrix is overdetermined, sparse, block banded and solved using fast iterative linear least squares solver. The simulation of turbulent flow over a backward step is in excellent agreement with the finite volume method using the same turbulent model.
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In this work, we propose and analyze a Morley-type virtual element method to approxi-mate the Stommel-Munk model in stream-function form. The discretization is based on the fully nonconforming virtual element approach presented in...
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In this work, we propose and analyze a Morley-type virtual element method to approxi-mate the Stommel-Munk model in stream-function form. The discretization is based on the fully nonconforming virtual element approach presented in Antonietti et al., (2018) and Zhao et al., (2018). The analysis restricts to simply connected polygonal domains, not necessarily convex. Under standard assumptions on the computational domain we derive some inverse estimates, norm equivalence and approximation properties for an enriching operator Eh defined from the nonconforming space into its H2-conforming counterpart. With the help of these tools we prove optimal error estimates for the stream-function in broken H2-, H1- and L2-norms under minimal regularity condition on the weak solution. Employing postprocessing formulas and adequate polynomial projections we compute from the discrete stream-function further fields of interest, such as: the velocity and vorticity. Moreover, for these postprocessed variables we establish error estimates. Finally, we report practical numerical experiments on different families of polygonal meshes.(c) 2022 Elsevier B.V. All rights reserved.
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