Composite Schemes for Conservation Laws

Liska, R.; Wendroff, Burton

doi:10.1137/s0036142996310976

Cited by 103 publications

(92 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Noh called this the wall heating problem. In [7] the Noh problem was done in Eulerian coordinates using the composite idea, and although there was a dip at the origin it was considerably less pronounced than that observed by Noh. This paper is a first attempt to see if the composite idea performs as well in Lagrangian coordinates, not just for the Noh problem but for a suite of test problems. We have found that for the Noh problem the composite scheme works about as well as it does in Eulerian coordinates, that is, there is a density dip but it is much less pronounced than for the standard code.…”

Section: Introductionmentioning

confidence: 90%

See 1 more Smart Citation

A Composite Scheme for Gas Dynamics in Lagrangian Coordinates

Shashkov

Wendroff

1999

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

One cycle of a composite finite difference scheme is defined as several time steps of an oscillatory scheme such as Lax-Wendroff followed by one step of a diffusive scheme such as Lax-Friedrichs. We apply this idea to gas dynamics in Lagrangian coordinates. We show numerical results in two dimensions for Noh's infinite strength shock problem and the Sedov blast wave problem, and for several one-dimensional problems including a Riemann problem with a contact discontinuity. For Noh's problem the composite scheme produces a better result than that obtained with a more conventional Lagrangian code.

show abstract

Section: Introductionmentioning

confidence: 90%

“…In [7,8] it is shown that an effective way to overcome this behavior of the two methods is to compose them. Thus, the composite scheme is defined by global composition of several LW steps followed by one LF step.…”

Section: Introductionmentioning

confidence: 99%

A Composite Scheme for Gas Dynamics in Lagrangian Coordinates

Shashkov

Wendroff

1999

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…(2) and (4), we are comparing the dissipation only. However, using the notion of composite schemes [5], the dispersion in a scheme is reduced by the inherent dissipation. A composite scheme made up of Lax-Wendroff and Lax-Friedrichs has better dispersive and dissipative properties than either Lax-Wendroff or LaxFriedrichs.…”

Section: Numerical Results For Experimentsmentioning

confidence: 99%

Computational Study of Three Numerical Methods for Some Linear and Non-Linear Advection-Diffusion-Reaction Problems

Appadu

Mphephu

2015

PCFD

View full text Add to dashboard Cite

In this paper, we use three existing schemes namely, Upwind Forward Euler, Non-Standard Finite Difference (NSFD) and Unconditionally Positive Finite Difference (UPFD) schemes to solve two numerical experiments described by a linear and a non-linear advection-diffusion-reaction equation with constant coefficients. These equations model exponential travelling waves and biofilm growth on a medical implant respectively. We study the exact and numerical dissipative and dispersive properties of the three schemes for both problems. Moreover, L 1 error, dispersion and dissipation errors, at some values of temporal and spatial step sizes have been computed for the three schemes for both problems.

show abstract

“…Suppressing of spurious oscillations is achieved by means of using a first-order Godunov step after each three second-order Lax-Wendroff steps. This idea of composition was invented by (Liska and Wendroff, 1998).…”

Section: Algorithm Descriptionmentioning

confidence: 99%

Stress-induced phase-transition front propagation in thermoelastic solids

Berezovski

Maugin

2005

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

A simplest possible mathematical model of martensitic phase transition front propagation is considered in the paper. Martensite and austenite phases are treated as isotropic linear thermoelastic materials. The phase transition front is viewed as an ideal mathematical discontinuity surface. Only one variant of martensite is involved. The problem remains nonlinear even in this simplified description that supposes a numerical solution. A non-equilibrium description of the process is provided by means of non-equilibrium jump relations at the moving phase boundary, which are formulated in terms of contact quantities. The same contact quantities are used in the construction of a finite-volume numerical scheme. The additional constitutive information is introduced by a certain assumption about the entropy production at the phase boundary. Results of numerical simulations show that the proposed approach allows us to capture experimental observations while corresponding to theoretical predictions in spite of the idealization of the process.

show abstract

Composite Schemes for Conservation Laws

Cited by 103 publications

References 14 publications

A Composite Scheme for Gas Dynamics in Lagrangian Coordinates

A Composite Scheme for Gas Dynamics in Lagrangian Coordinates

Computational Study of Three Numerical Methods for Some Linear and Non-Linear Advection-Diffusion-Reaction Problems

Stress-induced phase-transition front propagation in thermoelastic solids

Contact Info

Product

Resources

About