Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids (original) (raw)
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37th Aerospace Sciences Meeting and Exhibit, 1999
A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the singlegrid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stern appendages and a high-lift configuration.
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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 .
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34th Aerospace Sciences Meeting and Exhibit, 1996
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33rd Aerospace Sciences Meeting and Exhibit, 1995
This paper describes recent improvements to a node-centered upwind finite volume scheme for the solution of the compressible Euler and Navier-Stokes equations on unstructured meshes. The improvements include a more accurate boundary integration procedure, which is consistent with the finite element approximation, and a new reconstruction scheme based on the consistent mass matrix iteration. Several numerical results are presented to demonstrate the performance of the proposed improvements. The numerical results indicate that the present scheme significantly improves the quality of numerical solutions with very little additional computational cost.
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A faced based unstructured finite volume is presented for the solution of the incompressible Navier-Stokes equation on unstructured triangular meshes. The numerical method is based on the stable side-centered arrangement of primitive variables in which the velocity vector components are located at edge mid-points, meanwhile the pressure term is placed at element centroids. A special attention is given to accurately evaluate the viscous terms at the mid-point of the control volume faces. The convected terms are evaluated using the least square upwind interpolations. The resulting algebraic equations are solved in a monolithic manner. The implementation of the preconditioned Krylov subspace algorithm, matrix-matrix multiplication and the restricted additive Schwarz preconditioner are carried out using the PETSc software package in order to improve the parallel performance. The numerical method is validated for the classical benchmark problem of lid-driven cavity in a square enclosure....
Pegase: A Navier-Stokes Solver for Direct Numerical Simulation of Incompressible Flows
International Journal for Numerical Methods in Fluids, 1997
A hybrid conservative finite difference/finite element scheme is proposed for the solution of the unsteady incompressible Navier-Stokes equations. Using velocity-pressure variables on a non-staggered grid system, the solution is obtained with a projection method based on the resolution of a pressure Poisson equation. The new proposed scheme is derived from the finite element spatial discretization using the Galerkin method with piecewise bilinear polynomial basis functions defined on quadrilateral elements. It is applied to the pressure gradient term and to the non-linear convection term as in the so-called group finite element method. It ensures strong coupling between spatial directions, inhibiting the development of oscillations during long-term computations, as demonstrated by the validation studies. Two-and three-dimensional unsteady separated flows with open boundaries have been simulated with the proposed method using Cartesian uniform mesh grids. Several examples of calculations on the backward-facing step configuration are reported and the results obtained are compared with those given by other methods.