Automatic hybrid-Cartesian grid generation for high-Reynolds number flows around complex geometries

Delanaye, Michel; Aftosmis, Michael J.; Berger, Marsha; Liu, Yen; Pulliman, T.

doi:10.2514/6.1999-777

Cited by 26 publications

(19 citation statements)

References 10 publications

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“…Barth and Linton [5] successfully used the containment dual volume instead of the median dual on stretched triangulated quadrilateral grids to compute viscous flows. Having applied the viscous term discretization to the Laplace operator, Delanaye et al [8] showed that a correction of the diamond-shaped control volume on Cartesian grids leads to the more positive scheme and obtained a robust discretization of the viscous terms in Navier-Stokes equations. Putti and Cordes [13] have proposed a modification of the control volume that allowed them to obtain the positive discretization of the Laplace equation on three-dimensional Delaunay meshes.…”

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confidence: 99%

Modification of A Finite Volume Scheme for Laplace's Equation

Petrovskaya¹

2001

SIAM J. Sci. Comput.

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Abstract. For Laplace's equation, we discuss whether it is possible to construct a linear positive finite volume (FV) scheme on arbitrary unstructured grids. Dealing with the arbitrary grids, we state a control volume which guarantees a positive FV scheme with linear reconstruction of the solution. The control volume is defined by a property of the analytical solution to the equation and does not depend on the grid geometry. For those problems where the choice of the control volume is prescribed a priori, we demonstrate how to improve positivity of the linear FV scheme by using corrected reconstruction stencils. The difficulties arising when grids with no geometric restrictions are used for the discretization are discussed. Numerical examples illustrating the developed approach to the stencil correction are given.Key words. Laplace's equation, finite volume scheme, positivity, stencil correction AMS subject classifications. 65N12, 74S10, 35J05PII. S1064827500368925 Introduction.A discrete Laplace operator is often considered to be a good model for investigating a discretization of partial differential equations which contain diffusion operator ∇·(D∇). Two important examples are given by convection-diffusion equations and Navier-Stokes equations with possible applications that include the problems of fluid dynamics, chemical engineering, and environmental pollution. For the numerical solution of these equations, what is desirable are discretization schemes which satisfy a discrete maximum principle (monotone schemes); otherwise one can expect strong oscillations or even divergency of the solution.There are two possible approaches for development of monotone schemes on unstructured grids. The first approach is to use the grids with some geometric constraints on the triangulation. It is well known that triangulations with no obtuse triangles allow us to construct monotone schemes. The relevant examples are given in [6,11]. However, nonobtuse triangulations can be used on very few practical problems. In the process of the grid generation it is often required to resolve some complicated features of the problem geometry that makes strict angle control to be difficult.Looking for a wider class of triangulations, in the two-dimensional case a Delaunay triangulation [10] is very attractive. For Laplace's equation, in the two-dimensional case the Delaunay triangulation provides positivity (that guarantees the discrete maximum principle) of the linear finite element/finite volume scheme (Barth [3]). This important property may be applied for the solution of a wide range of problems, even more general than discretization of the Laplace equation. For instance, Xu and Zikatanov [17] developed a linear monotone finite element scheme for convectiondiffusion equations in any spatial dimension. To obtain a positive discretization of the diffusion operator they assumed the restrictive geometrical conditions which in the two-dimensional case mean that the triangulation is a Delaunay triangulation.

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confidence: 99%

Modification of A Finite Volume Scheme for Laplace's Equation

Petrovskaya¹

2001

SIAM J. Sci. Comput.

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“…Another significant automatic two-mesh approach is discussed in [2]. Here, the off-body meshing system is AMR based.…”

Section: Introductionmentioning

confidence: 99%

MOSS: multiple orthogonal strand system

Haimes

2014

Engineering with Computers

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This paper describes an overset approach that comprised virtual boundary-layer-like near-body grid coupled with an off-body adaptive mesh refinement farfield mesh for viscous fluids simulations. Unlike most a priori grid generation systems for the Reynolds-Averaged Navier-Stokes equations, the strand meshing paradigm is automatic, fast and requires little memory to provide boundary-layer coverage. In addition, the stacks of elements implied by the strands can be used to the simulation's advantage, where they naturally provide a line direction for semi-implicit solving.

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“…Even with this scheme, nonpositivity can still lead to convergence problems. Other authors have recently proposed modifications to the diamond path to reduce these problems [4].…”

Section: Viscous Flux Discretizationmentioning

confidence: 99%

“…Some authors have proposed using a hybrid of highly anisotropic body-fitted grids in the regions close to embedded bodies and Cartesian grids elsewhere [4], although this approach gives up much of the simplicity and elegance of the Cartesian grid method. A partial solution to the viscous boundary layer problem is the introduction of anisotropic refinement of the Cartesian cells.…”

Section: Introductionmentioning

confidence: 99%