Implicit space?time residual distribution method for unsteady laminar viscous flow

Dobe, Josef

doi:10.1016/s0045-7930(04)00033-7

Cited by 2 publications

(2 citation statements)

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“…One of the strategies followed in the past has been to work on highly implicit variants of the schemes, trying to cover this computational overhead with the possibility of using large time steps. Unfortunately, despite the excellent results, the schemes obtained in this way are relatively cumbersome to code [12,34,58,39].…”

Section: Generalizationmentioning

confidence: 99%

Hyperbolic balance laws: residual distribution, local and global fluxes

Abgrall¹,

Ricchiuto²

2021

Preprint

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This review paper describes a class of scheme named "residual distribution schemes" or "fluctuation splitting schemes". They are a generalization of Roe's numerical flux [61] in fluctuation form. The so-called multidimensional fluctuation schemes have historically first been developed for steady homogeneous hyperbolic systems. Their application to unsteady problems and conservation laws has been really understood only relatively recently. This understanding has allowed to make of the residual distribution framework a powerful playground to develop numerical discretizations embedding some prescribed constraints. This paper describes in some detail these techniques, with several examples, ranging from the compressible Euler equations to the Shallow Water equations.

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Section: Generalizationmentioning

confidence: 99%

Hyperbolic balance laws: residual distribution, local and global fluxes

Abgrall¹,

Ricchiuto²

2021

Preprint

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“…It is noted that different forms of distribution matrices can be used as stated in References [14][15][16] but numerical experience shows that using different forms of distribution matrix does not change the solutions appreciably, especially when steady state solutions are seeked. With a trivial algebra, one can show that the viscous source terms given in Equation (58) can be written as ( /4 T ) 3 j=1 n ·n j W j .…”

Section: Spatial Discretization: Matrix Distributionmentioning

confidence: 99%

A visual incompressible magneto‐hydrodynamics solver with radiation, mass, and heat transfer

Aslan

2009

Numerical Methods in Fluids

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SUMMARYA visual two-dimensional (2D) nonlinear magneto-hydrodynamics (MHD) code that is able to solve steady state or transient charged or neutral convection problems under the radiation, mass, and heat transfer effects is presented. The flows considered are incompressible and the divergence conditions on the velocity and magnetic fields are handled by similar relaxation schemes in the form of pseudo-iterations between the real time levels. The numerical method utilizes a matrix distribution scheme that runs on structured or unstructured triangular meshes. The time-dependent algorithm developed here utilizes a semi-implicit dual time stepping technique with multistage Runge-Kutta (RK) algorithm. It is possible for the user to choose different normalizations (natural, forced, Boussinesq, Prandtl, double-diffusive and radiation convection) automatically. The code is visual and runs interactively with the user. The graphics algorithms work multithreaded and allow the user to follow certain flow features (color graphs, vector graphs, one-dimensional profiles) during runs, see (Comput. Fluids 2007; 36:961-973) for details. With the code presented here nonlinear steady or time-dependent evolution of heated and stratified neutral and charged liquids, convection of mixture of neutral and charged gases, double-diffusive and salinity natural convection flows with internal heat generation/absorption and radiative heat transfer flows can be investigated. In addition, the numerical method (combining concentration, radiation, heat transfer, and MHD effects) takes the advantage of local time stepping and employs simplified residual jacobian matrix to increase pseudo-convergence rate. This code is currently being improved to simulate three-dimensional problems with parallel processing.

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Implicit space?time residual distribution method for unsteady laminar viscous flow

Cited by 2 publications

References 0 publications

Hyperbolic balance laws: residual distribution, local and global fluxes

Hyperbolic balance laws: residual distribution, local and global fluxes

A visual incompressible magneto‐hydrodynamics solver with radiation, mass, and heat transfer

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