A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid
01 Jan 2003-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 184, Iss: 1, pp 1-36
TL;DR: In this article, a method for representing curved boundaries for the solution of the Navier-Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid is presented.
About: This article is published in Journal of Computational Physics.The article was published on 2003-01-01. It has received 206 citations till now. The article focuses on the topics: Navier–Stokes equations & Boundary value problem.
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01 Nov 2002
TL;DR: An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented in this paper, where a boundary condition is enforced through a ghost cell method.
Abstract: An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.
740 citations
Cites methods from "A representation of curved boundari..."
...[24] present a second-order accurate IBM on a non-uniform, staggered three-dimensional Cartesian grid....
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TL;DR: An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented in this article, where a boundary condition is enforced through a ghost cell method.
674 citations
TL;DR: In this paper, a numerical method is developed for solving the Navier-Stokes equations in Cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics.
534 citations
Cites background or methods from "A representation of curved boundari..."
...Implementing a pure staggered grid discretization in a Cartesian grid approach, however, would be cumbersome due to need for special treatment of grid nodes near the body – see [19] for a recent extensive discussion on the difficulties encountered in the implementation of a staggered grid approach in a Cartesian method....
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...Cut-cell formulations applicable to three-dimensional problems with stationary immersed boundaries have been proposed in [16–18] and [19]....
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TL;DR: The proposed cut-cell based approach to reducing spurious pressure oscillations observed when simulating moving boundary flow problems with sharp-interface immersed boundary methods is shown to retain all the desirable properties of the original finite-difference based IBM while at the same time, reducing pressure oscillation for moving boundaries by roughly an order of magnitude.
353 citations
Additional excerpts
...[18] used ‘cell-linking’ technique instead of ‘merging’, and Meyer et al....
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TL;DR: Different IB approaches for imposing boundary conditions, efficient iterative algorithms for solving the incompressible Navier–Stokes equations in the presence of dynamic immersed boundaries, and strong and loose coupling FSI strategies are summarized and juxtapose.
336 citations
References
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Book•
01 Jan 1996
TL;DR: This text develops and applies the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice, including advanced techniques in computational fluid dynamics.
Abstract: Preface. Basic Concepts of Fluid Flow.- Introduction to Numerical Methods.- Finite Difference Methods.- Finite Volume Methods.- Solution of Linear Equation Systems.- Methods for Unsteady Problems.- Solution of the Navier-Stokes Equations.- Complex Geometries.- Turbulent Flows.- Compressible Flow.- Efficiency and Accuracy Improvement. Special Topics.- Appendeces.
7,066 citations
TL;DR: In this paper, a convective modeling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencings.
4,190 citations
01 Jan 1979
2,299 citations
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01 Jan 1995
TL;DR: A Thomas's algorithm for the solution of a tridiagonal system of Equations is described in this paper, as well as a detailed discussion of the future of Computational Fluid Dynamics.
Abstract: Part I*Basic Thoughts and Equations 1 Philosophy of Computational Fluid Dynamics 2 The Governing Equations of Fluid Dynamics Their Derivation, A Discussion of Their Physical Meaning, and A Presentation of Forms Particularly Suitable to CFD 3 Mathematical Behavior of Partial Differential Equations The Impact on Computational Fluid Dynamics Part II*Basics of the Numerics 4 Basic Aspects of Discretization 5 Grids and Meshes, With Appropriate Transformations 6 Some Simple CFD Techniques A Beginning Part III*Some Applications 7 Numerical Solutions of Quasi-One-Dimensional Nozzle Flows 8 Numerical Solution of A Two-Dimensional Supersonic Flow Prandtl-Meyer Expansion Wave 9 Incompressible Couette Flow Numerical Solution by Means of an Implicit Method and the Pressure Correction Method 10 Incompressible, Inviscid Slow Over a Circular Cylinder Solution by the Technique Relaxation Part IV*Other Topics 11 Some Advanced Topics in Modern CFD A Discussion 12 The Future of Computational Fluid Dynamics Appendixes A Thomas's Algorithm for the Solution of A Tridiagonal System of Equations References
1,738 citations
"A representation of curved boundari..." refers methods in this paper
...Discussions of these techniques can be found in [10, 11 ]....
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TL;DR: In this paper, a second-order projection method for the Navier-Stokes equations is proposed, which uses a specialized higher-order Godunov method for differencing the nonlinear convective terms.
1,287 citations