Numerical simulations of unsteady viscous incompressible flows using general pressure equation (original) (raw)
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International Journal for Numerical Methods in Fluids, 2008
In this work, artificial compressibility method is used to solve steady and unsteady flows of viscous incompressible fluid. The method is based on implicit higher-order upwind discretization of Navier-Stokes equations. The extension for unsteady simulation is considered by increasing artificial compressibility parameter or by using dual time stepping. Turbulence models are eddy-viscosity SST model and explicit algebraic Reynolds stress model. Results for steady turbulent flow over confined backward-facing step, unsteady laminar flow around circular cylinder and for unsteady turbulent free synthetic jet are presented.
A Numerical Method for the Solution of Compressible and Incompressible Fluid Flows
1995
Numerical simulation plays nowadays an important role to predict the flow field in many situations. To design a new mechanical device involving fluid dynamics, a numerical simulation is well accepted and justified. However, many work still remains to improve the numerical methods towards a fast, accurate and stable convergence. This work presents efficiency studies to solve compressible and incompressible fluid flows using a finite-volume, explicit Runge-Kutta multistage scheme, with central spatial discretization in combination with multigrid. An extension of the methodology normally employed to solve compressible flows is used to solve incompressible flow problems. Numerical results are presented for a cylinder and the NACA 0012 airfoil for Mach-numbers ranging from 0.8 to 0.005 using the Euler equations.
Journal of Computational Physics, 1996
tions, and requires intense interpolations. Thus, ever since the collocated grid arrangement was proposed [5], stag-Pressure-based and artificial compressibility methods for calculating three-dimensional, steady, incompressible viscous flows are gered grids have seldomly been used, while collocated grids compared in this work. Each method is applied to the prediction of are being increasingly applied to recent studies [10][11][12]. three-dimensional, laminar flows in strongly curved ducts of square Nevertheless, there are certainly some critical issues that and circular cross sections. Numerical predictions from each require attention when using the collocated grid arrangemethod are compared with available experimental data and prement, for instance, one might need artificial damping terms, viously reported predictions using a multigrid numerical method. The accuracy, grid independence, convergence behavior, and comor a special cell face interpolation technique to avoid the putational efficiency of each method are critically examined. Hence, checkerboard problem .
International Journal for Numerical Methods in Engineering, 2002
In Part I of this paper, a preconditioned artiÿcial compressibility scheme was developed for modelling laminar steady-state and transient, incompressible ows for a wide range of Reynolds and Rayleigh numbers. In this part, several examples of laminar incompressible problems are solved and discussed. The in uence of various AC parameters on robustness and convergence rates are assessed for a complex category of problems. It is shown that the scheme developed in Part I is an accurate, robust and easy to use method for solving incompressible laminar ow problems over a wide range of ow regimes.
Journal of Computational Physics, 2010
The artificial compressibility method for the incompressible Navier-Stokes equations is revived as a high order accurate numerical method (4th order in space and 2nd order in time). Similar to the lattice Boltzmann method, the mesh spacing is linked to the Mach number. The accuracy higher than that of the lattice Boltzmann method is achieved by exploiting the asymptotic behavior of solution of artificial compressibility equations for small Mach numbers and the simple lattice structure of stencil. An easy method for quickening the decay of acoustic waves, which deteriorate the quality of numerical solution, and a simple cure for the checkerboard instability are proposed there. The high performance of the scheme is demonstrated not only for the periodic boundary condition but also for the Dirichlet-type boundary condition.
Applied Mathematics and Computation, 2008
A computational code is developed using cell-centered finite volume method with a nonuniform grid for solving the incompressible viscous and inviscid flows. The method has been used to determine the steady incompressible inviscid flows past a cylinder in free stream, the steady incompressible inviscid flows past a circular bump through a channel, and also the steady incompressible viscous flows past a backward facing-step. In this method, the 2D Navier-Stokes equations (or 2D incompressible Euler equations for inviscid flow), which are modified by artificial compressibility and preconditioning concepts, are solved with the Jameson's artificial dissipation and viscosity terms under the form of a fourth-and second-order x-derivative, respectively. An explicit fourth-order Runge-Kutta integration algorithm is applied to find the steady state condition. The effects of CFL number, artificial viscosity coefficient, and pseudo-compressibility parameter in convergence of solution are investigated.
A Study of Numerical Schemes for Incompressible Fluid Flows
TEMA - Tendências em Matemática Aplicada e Computacional, 2005
The present work is concerned with a study of numerical schemes for solving two-dimensional time-dependent incompressible free-surface fluid flow problems. The primitive variable flow equations are discretized by the finite difference method. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The diffusive terms are discretized by Implicit Backward and Crank-Nicolson schemes, and the non-linear advection terms are approximated by the high order upwind VONOS (Variable-Order Non-oscillatory Scheme) technique. In order to improved numerical stability of the schemes, the boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical schemes are then applied to the simulation of the Hagen-Poiseuille flow, and container filling problems. The results show that the semi-implicit techniques eliminate the stability restriction in the original explicit GENSMAC method.
Numerical methods for incompressible viscous flow
Advances in Water Resources, 2002
We present an overview of the most common numerical solution strategies for the incompressible Navier-Stokes equations, including fully implicit formulations, artificial compressibility methods, penalty formulations, and operator splitting methods (pressure/velocity correction, projection methods). A unified framework that explains popular operator splitting methods as special cases of a fully implicit approach is also presented and can be used for constructing new and improved solution strategies. The exposition is mostly neutral to the spatial discretization technique, but we cover the need for staggered grids or mixed finite elements and outline some alternative stabilization techniques that allow using standard grids. Emphasis is put on showing the close relationship between (seemingly) different and competing solution approaches for incompressible viscous flow.