Improved shock‐capturing of Jameson's scheme for the Euler equations

Burg, J.W. van der; Kuerten, Johannes G.M.; Zandbergen, P.J.

doi:10.1002/fld.1650150603

Cited by 13 publications

(3 citation statements)

References 8 publications

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“…Here, L and R are the matrices of which the columns are the left and right eigenvectors of A; L = R −1 . The matrices L and R are given below [31]…”

Section: One-dimensional Euler Solvermentioning

confidence: 99%

CFD Julia: A Learning Module Structuring an Introductory Course on Computational Fluid Dynamics

Pawar

San

2019

Fluids

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CFD Julia is a programming module developed for senior undergraduate or graduate-level coursework which teaches the foundations of computational fluid dynamics (CFD). The module comprises several programs written in general-purpose programming language Julia designed for high-performance numerical analysis and computational science. The paper explains various concepts related to spatial and temporal discretization, explicit and implicit numerical schemes, multi-step numerical schemes, higher-order shock-capturing numerical methods, and iterative solvers in CFD. These concepts are illustrated using the linear convection equation, the inviscid Burgers equation, and the two-dimensional Poisson equation. The paper covers finite difference implementation for equations in both conservative and non-conservative form. The paper also includes the development of one-dimensional solver for Euler equations and demonstrate it for the Sod shock tube problem. We show the application of finite difference schemes for developing two-dimensional incompressible Navier-Stokes solvers with different boundary conditions applied to the lid-driven cavity and vortex-merger problems. At the end of this paper, we develop hybrid Arakawa-spectral solver and pseudo-spectral solver for two-dimensional incompressible Navier-Stokes equations. Additionally, we compare the computational performance of these minimalist fashion Navier-Stokes solvers written in Julia and Python.

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“…Here, L and R are the matrices of which the columns are the left and right eigenvectors of A; L = R −1 . The matrices L and R are given below [31]…”

Section: One-dimensional Euler Solvermentioning

confidence: 99%

CFD Julia: A Learning Module Structuring an Introductory Course on Computational Fluid Dynamics

Pawar

San

2019

Fluids

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“…Similar quantities are also defined for the q coordinate direction. These terms are combined with the cell-based residual terms to give the nodal residual When four cells meet at a common vertex, the overall effect of the distribution of the artificial viscosity vector is to add a scaled second and fourth-difference to the node-based equation (12).…”

Section: Numerical Dissipationmentioning

confidence: 99%

An investigation of artificial dissipation for the cell‐vertex finite volume method

Mackenzie

1995

Numerical Methods in Fluids

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SUMMARYThis paper is concerned with an investigation of artificial dissipation models that are used with the cell-vertex finite volume approximation of the compressible Euler and Navier-Stokes equations. Based on the observation that first and second-order upwind schemes can be written as a central discretization plus an appropriately scaled dissipative flux, a matrix scaling of second and fourth-differences is implemented in an artificial dissipation model that also uses a procedure to limit the applicability of shock-capturing dissipation. Analysis of the model and the associated boundary conditions is given to determine the effect on accuracy. Numerical results are given for transonic Euler flow past a NACA0012 aerofoil profile which demonstrate the improved shock-capturing capability of the model. Results for laminar subsonic viscous flow over a flat plate show that the matrix-dissipation model reduces the amount of spurious artificial dissipation within boundary layers.

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“…However, the decrease of artificial dissipation leads to a better c~ption of the physical phenomena in the solution, which would otherwise require a finer grid. Shock waves can be captured more accurately, if the first order difference terms in the artificial dissipation, which are triggered by a shock sensor, are replaced by upwind differences [6]. This approach works both for inviscid and turbulent, viscous flow problems (see figure 2).…”

Section: Artificial Dissipationmentioning

confidence: 99%