An evaluation of several differencing methods for inviscid fluid flow problems

Emery, A. F.

doi:10.1016/0021-9991(68)90060-0

Cited by 164 publications

(84 citation statements)

References 8 publications

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“…A challenging test for computing unsteady shock waves is the numerical simulation of a wind tunnel with a flat faced step, originally introduced in [44] to compare several difference schemes in classical fluid dynamics. It is now a standard numerical benchmark (see, e.g.…”

Section: The Forward-facing Step Problemmentioning

confidence: 99%

A simple shock‐capturing technique for high‐order discontinuous Galerkin methods

Huerta

Casoni

Peraire

2011

Numerical Methods in Fluids

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This is the accepted version of the following article: [Huerta, A., Casoni, E. and Peraire, J. (2012), A simple shock-capturing technique for high-order discontinuous Galerkin methods. Int. J. Numer. Meth. Fluids, 69: 1614–1632. doi:10.1002/fld.2654], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/fld.2654/fullThis article presents a novel shock-capturing technique for the discontinuous Galerkin (DG) method. The technique is designed for compressible flow problems, which are usually characterized by the presence of strong shocks and discontinuities. The inherent structure of standard DG methods seems to suggest that they are especially adapted to capture shocks because of the numerical fluxes based on suitable approximate Riemann solvers, which, in practice, introduces some stabilization. However, the usual numerical fluxes are not sufficient to stabilize the solution in the presence of shocks for large high-order elements. Here, a new basis of shape functions is introduced. It has the ability to change locally between a continuous or discontinuous interpolation depending on the smoothness of the approximated function. In the presence of shocks, the new discontinuities inside an element introduce the required stabilization because of numerical fluxes. Large high-order elements can therefore be used and shocks captured within a single element, avoiding adaptive mesh refinement and preserving the locality and compactness of the DG scheme. Several numerical examples for transonic and supersonic flows are studied to demonstrate the applicability of the proposed approach.Peer ReviewedPostprint (author's final draft

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Section: The Forward-facing Step Problemmentioning

confidence: 99%

A simple shock‐capturing technique for high‐order discontinuous Galerkin methods

Huerta

Casoni

Peraire

2011

Numerical Methods in Fluids

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“…One may consider the channel to be a stylized engine inlet of a supersonic aircraft. In fact it is just a benchmark geometry [34,35]. The red vertical valve in the bottom of the channel instantaneously snaps up, such that, together with the red horizontal plate, it forms a step which suddenly chokes part of the channel.…”

Section: An Examplementioning

confidence: 99%

Computational fluid dynamics: Science and tool

Koren

2006

The Mathematical Intelligencer

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“…The forward-facing step problem was introduced by Emery 3 and later used, among others, by Woodward and Colella 13 . The problem starts with a Mach 3 flow in a wind tunnel section.…”

Section: Forward-facing Stepmentioning

confidence: 99%

A Simple and Efficient Space-Time Adaptive Grid Technique for Unsteady Compressible Flows

Wackers

Koren

2003

16th AIAA Computational Fluid Dynamics Conference

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C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a MAS Modelling, Analysis and Simulation Modelling, Analysis and SimulationThe technique is applied to the 2D unsteady Euler equations. The method is relatively simple, computationally very efficient and it can be easily adapted to other types of fluid flow. It consists of four parts: (i) a time-stepping algorithm that adapts the grid to the solution several times per coarse time step, (ii) a second-order accurate discretisation of the flow equations that combines a limited upwind discretisation of the fluxes with a two-step discretisation of the time derivatives and is well-suited for adapted grids, (iii) a simple data structure to store the solution and the grid geometry, and (iv) a refinement criterion. Two of these are tested, one based on the first and one on the second spatial derivative of the density. Results for two test problems, the classical forwardfacing step problem and the shedding of vorticity from a flat plate, show that the method is much more efficient than comparable methods without adaptive gridding. ABSTRACTA space-time adaptive gridding technique for unsteady flows is presented. The technique is applied to the 2D unsteady Euler equations. The method is relatively simple, computationally very efficient and it can be easily adapted to other types of fluid flow. It consists of four parts: (i) a time-stepping algorithm that adapts the grid to the solution several times per coarse time step, (ii) a second-order accurate discretisation of the flow equations that combines a limited upwind discretisation of the fluxes with a two-step discretisation of the time derivatives and is well-suited for adapted grids, (iii) a simple data structure to store the solution and the grid geometry, and (iv) a refinement criterion. Two of these are tested, one based on the first and one on the second spatial derivative of the density. Results for two test problems, the classical forward-facing step problem and the shedding of vorticity from a flat plate, show that the method is much more efficient than comparable methods without adaptive gridding.

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An evaluation of several differencing methods for inviscid fluid flow problems

Cited by 164 publications

References 8 publications

A simple shock‐capturing technique for high‐order discontinuous Galerkin methods

A simple shock‐capturing technique for high‐order discontinuous Galerkin methods

Computational fluid dynamics: Science and tool

A Simple and Efficient Space-Time Adaptive Grid Technique for Unsteady Compressible Flows

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