A review and comparative study of upwind biased schemes for compressible flow computation. Part III: Multidimensional extension on unstructured grids

Lyra, Paulo Roberto Maciel; Morgan, K.

doi:10.1007/bf02818932

Cited by 38 publications

(44 citation statements)

References 83 publications

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“…Figure 4, shows the pressure and Mach isoregions and the formation of a shock wave, for a Mach 3:0 ow. The results compare well with those published in, for example, Reference [11]. …”

Section: Numerical Resultssupporting

confidence: 88%

A stabilized finite element formulation to solve high and low speed flows

Costa

Lyra

2005

Commun. Numer. Meth. Engng.

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SUMMARYIt is well known that numerical methods designed to solve the compressible Euler equations, when written in terms of conservation variables behave poorly in the incompressible limit, that is, when density variations are negligible. However, a change to pressure based variables seem to, partly, eliminate the problem by making the Jacobian matrices fully invertible whatever the ow regime may be. Despite this apparent beneÿt, the stabilization matrix plus discontinuity capturing operator (for the compressible regime) still need attention, since they tend to be ill behaved for either conservation or pressure variables. In this paper, we introduce a simple way of balancing two stabilizing matrices, one of them suitable for low Mach ows and the other one for supersonic ows, so that a wide range of ow regimes are covered with only one formulation. Comparison between conservation and pressure variables is made and numerical examples are shown to validate the method.

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“…Figure 4, shows the pressure and Mach isoregions and the formation of a shock wave, for a Mach 3:0 ow. The results compare well with those published in, for example, Reference [11]. …”

Section: Numerical Resultssupporting

confidence: 88%

A stabilized finite element formulation to solve high and low speed flows

Costa

Lyra

2005

Commun. Numer. Meth. Engng.

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“…The resulting Mach number contours and the C p plot are presented in Figure 12(a) and 12(b), respectively. Compared with available numerical results (Caraeni & Fuchs, 2002;Chassaing, Khelladi, & Nogueira, 2013;Lyra & Morgan, 2002), reasonably accurate results are obtained using the present GPU-based meshless solvers.…”

Section: Viscous Flow Over Naca0012 Airfoilmentioning

confidence: 64%

A graphics processing unit-accelerated meshless method for two-dimensional compressible flows

Zhang

Chen

Cao

2017

Engineering Applications of Computational Fluid Mechanics

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A graphics processing unit (GPU) -accelerated meshless method is presented for solving twodimensional compressible flows over aerodynamic bodies. The Compute Unified Device Architecture (CUDA) Fortran programming model is employed to port the meshless method from central processing unit to GPU as a way of achieving efficiency, which involves implementation of CUDA kernels and management of data storage structure and thread hierarchy. The CUDA kernel subroutines are designed to meet with the point-based computing of the meshless method. The corresponding point-based data structure and thread hierarchy are constructed or manipulated in the paper by presenting two specific GPU implementations of the meshless method, which are developed for solving Navier-Stokes equations. The Jameson-Schmidt-Turkel scheme is used to estimate the flux terms of the Navier-Stokes equations and an explicit four-stage Runge-Kutta scheme is applied to update the solution at time level. After tuning the performances of the resulting two GPU-accelerated meshless solvers by changing the number of threads in a block, a set of typical flows over aerodynamic bodies are simulated for validation. Numerical results are shown in a comparison with available experimental data or computational values that appear in extant literature with an analysis of code performance. This reveals that the cost of computing time of the presented test cases is significantly reduced for both solvers without losing accuracy, while impressive speedups up to 64 times are achieved due to careful management of memory access. ARTICLE HISTORY

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“…In cases where coincidence or near coincidence is detected between the extrapolated edge and an upwind tetrahedral face or edge the limiting is collapsed to be entirely face or edge based. A similar convex average interpolant is constructed with respect to vertex k using the right hand tetrahedra T D to obtain the difference S dk together with analogous limiter bounds that now depend on the edge slopes S 4k , S 5k and S 6k ensuring a maximum principle with min S S R max S over T D and edge e. This scheme is a three-dimensional generalization of the higher order scheme presented in Reference [3] and is similar in motivation to the local edge diminishing (LED) schemes of References [34,35], with a higher order reconstruction applied to the data, (saturation field in this case). The second step of the scheme uses the upwind flux where each higher order approximation of phase saturation is upwinded via the flux using Equations (19), (21) in Equation (17).…”

Section: Higher Order Schemesmentioning

confidence: 87%

Higher‐resolution hyperbolic‐coupled‐elliptic flux‐continuous CVD schemes on structured and unstructured grids in 3‐D

Edwards

2006

Numerical Methods in Fluids

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SUMMARYNovel three-dimensional unstructured grid higher order convection schemes are presented. The schemes are coupled with locally conservative flux continuous control-volume distributed (CVD) finite-volume schemes for the porous medium general tensor pressure equation on structured and unstructured grids in 3-D.The schemes are developed for multi-phase flow in porous media. Benefits of the schemes in terms of improved front resolution and medium discontinuity resolution are demonstrated. Comparisons with current methods including the control-volume finite element method highlight the advantages of the new formulation for three-dimensional reservoir simulation.

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A review and comparative study of upwind biased schemes for compressible flow computation. Part III: Multidimensional extension on unstructured grids

Cited by 38 publications

References 83 publications

A stabilized finite element formulation to solve high and low speed flows

A stabilized finite element formulation to solve high and low speed flows

A graphics processing unit-accelerated meshless method for two-dimensional compressible flows

Higher‐resolution hyperbolic‐coupled‐elliptic flux‐continuous CVD schemes on structured and unstructured grids in 3‐D

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