A weighted least square scheme for compressible flows

Fürst, Jiří

doi:10.1007/s10494-006-9021-y

Cited by 12 publications

(7 citation statements)

References 12 publications

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“…We note in passing that the idea of employing least squares fitting of the data in the same context has been exploited, in different fashions, at least in [1,14,23]. Following the same procedure as in the one dimensional case, we introduce four linear functions Pγ , γ = 1, .…”

Section: Cweno Reconstruction In 2d Adaptive Gridmentioning

confidence: 99%

Adaptive Mesh Refinement for Hyperbolic Systems Based on Third-Order Compact WENO Reconstruction

2015

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In this paper we generalize to non-uniform grids of quad-tree type the Compact WENO reconstruction of Levy, Puppo and Russo (SIAM J. Sci. Comput., 2001), thus obtaining a truly two-dimensional non-oscillatory third order reconstruction with a very compact stencil and that does not involve mesh-dependent coefficients. This latter characteristic is quite valuable for its use in h-adaptive numerical schemes, since in such schemes the coefficients that depend on the disposition and sizes of the neighboring cells (and that are present in many existing WENO-like reconstructions) would need to be recomputed after every mesh adaption.In the second part of the paper we propose a third order h-adaptive scheme with the above-mentioned reconstruction, an explicit third order TVD RungeKutta scheme and the entropy production error indicator proposed by Puppo and Semplice (Commun. Comput. Phys., 2011). After devising some heuristics on the choice of the parameters controlling the mesh adaption, we demonstrate with many numerical tests that the scheme can compute numerical solution whose error decays as N −3 , where N is the average number of cells used during the computation, even in the presence of shock waves, by making a very effective use of h-adaptivity and the proposed third order reconstruction.

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Section: Cweno Reconstruction In 2d Adaptive Gridmentioning

confidence: 99%

Adaptive Mesh Refinement for Hyperbolic Systems Based on Third-Order Compact WENO Reconstruction

2015

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“…For the purpose of comparison, we shall use both linear and quadratic interpolation. We stress that building more accurate and stable semi-Lagrangian methods, for example, based on non-linear oscillatory-free interpolation procedures [28], may be another way of developing staggered octree grid schemes. However, such developments are not within the scope of the present paper.…”

Section: Numerical Time-integrationmentioning

confidence: 99%

An octree-based solver for the incompressible Navier–Stokes equations with enhanced stability and low dissipation

Olshanskii¹,

Terekhov²,

Vassilevski³

2013

Computers & Fluids

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The paper introduces a finite difference solver for the unsteady incompressible Navier-Stokes equations based on adaptive cartesian octree grids. The method extends a stable staggered grid finite difference scheme to the graded octree meshes. It is found that a straightforward extension is prone to produce spurious oscillatory velocity modes on the fine-to-coarse grids interfaces. A local linear low-pass filter is shown to reduce much of the bad influence of the interface modes on the accuracy of numerical solution. We introduce an implicit upwind finite difference approximation of advective terms as a low dissipative and stable alternative to semi-Lagrangian methods to treat the transport part of the equations. The performance of method is verified for a set of benchmark tests: a Beltrami type flow, the 3D lid-driven cavity and channel flows over a 3D square cylinder.

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“…For interpolation we use a modification of the conservative weighted least-squares (WLSQR) reconstruction [9]. Assume that in a cell T 0 and in the neighbouring cells T i the piecewise constant function u be given by values u 0 and u i .…”

Section: Water Flooding Simulations On Dynamic Octreesmentioning

confidence: 99%

“…We treat high gradients of water saturation as the sharp front between two phases and high gradients of oil pressure as peculiarities of Darcy's velocities. For interpolation of data between two nested grids we use local conservative interpolation [9].…”

mentioning

confidence: 99%

Two-phase water flooding simulations on dynamic adaptive octree grids with two-point nonlinear fluxes

Terekhov

Vassilevski

2013

Russian Journal of Numerical Analysis and Mathematical Modelling

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We present a method for numerical simulation of the two-phase water flooding problem on general polyhedral grids not aligned with permeability tensor K (K-nonorthogonal grids) and dynamic octree grids adapted to the front between the phases. The discretization is based on the cell-centered monotone finite volume (FV) method with the nonlinear two-point flux approximation (TPFA) applicable to general K-non-orthogonal polyhedral grids. We use fully implicit discretization in time to avoid the restriction on the time step caused by the minimal mesh size. In our numerical experiments we demonstrate the superiority of the nonlinear TPFA on a K-non-orthogonal grid over linear TPFA and considerable speed-up of the simulation on a dynamically adapted octree grid with minimal loss in accuracy compared to the simulation on a fine regular grid. Two-phase water flooding is the secondary stage of oil recovery represented by the two-phase black oil model equations. At this stage, water is injected into injector wells, while oil is produced through producer wells. In twophase water flooding simulation, appropriate recovery of the moving water front is very important. The presence of the full essentially anisotropic permeability tensor K and grids not aligned with the tensor K (K-nonorthogonal grids) and the computer memory restriction on the minimal grid size transform the numerical simulation into a challenge. We use two approaches to this challenge: the nonlinear finite volume (FV) method and the Rosatom project 'Breakthrough'. Brought to you by | HEC Bibliotheque Maryriam ET J. Authenticated Download Date | 6/8/15 5:28 AM cUsing (4.2) and (4.3) we get the following representation for the flux varia-Brought to you by | HEC Bibliotheque Maryriam ET J. Authenticated Download Date | 6/8/15 5:28 AM

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A weighted least square scheme for compressible flows

Cited by 12 publications

References 12 publications

Adaptive Mesh Refinement for Hyperbolic Systems Based on Third-Order Compact WENO Reconstruction

Adaptive Mesh Refinement for Hyperbolic Systems Based on Third-Order Compact WENO Reconstruction

An octree-based solver for the incompressible Navier–Stokes equations with enhanced stability and low dissipation

Two-phase water flooding simulations on dynamic adaptive octree grids with two-point nonlinear fluxes

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