# High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws

@article{Sweby1984HighRS, title={High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws}, author={Peter K. Sweby}, journal={SIAM Journal on Numerical Analysis}, year={1984}, volume={21}, pages={995-1011} }

The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is expl...

## 2,338 Citations

### Flux limiters fourth and sixth order high resolution method for hyperbolic conservation laws

- MathematicsInt. J. Comput. Math.
- 2000

The technique of obtaining high resolution, total variation non increasing oscillation free and explicit scalar difference scheme is derived by adding multi-limiters of antidiffusive flux to a first order scheme.

### On the convergence of high resolution methods with multiple time scales for hyperbolic conservation laws

- MathematicsMath. Comput.
- 2003

A maximum principle and the TVD property are verified for general advective flux and an entropy condition is verified which, with sufficient limiting, guarantees convergence to the entropy solution for convex flux.

### Flux difference splitting for hyperbolic systems of conservation laws with source terms

- Mathematics, Physics
- 1993

### Simple High-Order Bounded Convection Scheme to Model Discontinuities

- Physics
- 1997

A new high-order-accurate convection scheme that satisfies the total variation diminishing (TVD) principle and is based on nonlinear functional relations between normalized variables is presented.…

### A New Time-space Accurate Scheme for Hyperbolic Problems I: Quasi-explicit Case

- Computer Science
- 1998

A new discretization scheme for hyperbolic systems of conservations laws satisfies the TVD property and relies on the new high-resolution mechanism which is compatible with the genuinely multidimensional approach proposed recently.

### On the numerical dissipation of high resolution schemes for hyperbolic conservation laws

- Mathematics
- 1988

### Second-order scheme for the scalar nonlinear conservation laws with flux depending on the space variable

- Physics, Mathematics
- 1997

### Limiting strategies for polynomial reconstructions in the finite volume approximation of the linear advection equation

- Mathematics
- 2004

### Second Order Positive Schemes by means of Flux Limiters for the Advection Equation

- Mathematics
- 2009

In this paper, we study rst and second order positive numerical methods for the advection equation. In particular, we consider the direct dis- cretization of the model problem and comment on its…

## References

SHOWING 1-10 OF 21 REFERENCES

### Riemann Solvers, the Entropy Condition, and Difference

- Computer Science
- 1984

A condition on the numerical flux for semidiscrete approximations to scalar, nonconvex conservation laws is introduced, and shown to guarantee convergence to the correct physical solution. An equal...

### Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme

- Mathematics
- 1974

### Numerical Viscosity and the Entropy Condition for Conservative Difference Schemes

- Computer Science
- 1984

It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation, and entropy satisfying convergence follows for E schemes - those containing more Numbers than Godunov's scheme.

### High Resolution Schemes and the Entropy Condition

- Mathematics
- 1984

A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five-point band width, approximations to scalar conservation laws, is presented. These schemes are…

### A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws

- Mathematics
- 1978

### Stable and entropy satisfying approximations for transonic flow calculations

- Physics
- 1980

Finite difference approximations for the small disturbance equation of transonic flow are developed and analyzed. New schemes of the Cole-Murman type are presented fpr which nonlinear stability is…

### High resolution applications of the Osher upwind scheme for the Euler equations

- Mathematics
- 1983

The 'Osher' scheme was introduced by Osher (1981). It represents an upwind finite-difference method for hyperbolic systems of conservation laws, including the Euler equations. In studies conducted by…

### Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works

- Computer Science
- 1973

### On convergence of monotone finite difference schemes with variable spatial differencing

- Mathematics
- 1983

Monotone finite difference schemes used to approximate solutions of scalar conservation laws have the advantage that these approximations can be proved to converge to the proper solution as the mesh…