High-resolution scheme

High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. They have the following properties:

*Second or higher order spatial accuracy is obtained in smooth parts of the solution.
*Solutions are free from spurious oscillations or wiggles.
*High accuracy is obtained around shocks and discontinuities.
*The number of mesh points containing the wave is small compared with a first-order scheme with similar accuracy.

High-resolution schemes often use flux/slope limiters to limit the gradient around shocks or discontinuities. A particularly successful high-resolution scheme is the MUSCL scheme which uses state extrapolation and limiters to achieve good accuracy - see diagram below.

Further reading

*Harten, A. (1983), High Resolution Schemes for Hyperbolic Conservation Laws. "J. Comput. Phys"., 49:357-293.
*Hirsch, C. (1990), "Numerical Computation of Internal and External Flows", vol 2, Wiley.
*Laney, Culbert B. (1998), "Computational Gas Dynamics", Cambridge University Press.
*Toro, E. F. (1999), "Riemann Solvers and Numerical Methods for Fluid Dynamics", Springer-Verlag.

ee also

*Flux limiter
*Godunov's theorem
*MUSCL scheme
*Sergei K. Godunov
*Total variation diminishing
*Shock capturing methods