A nonoscillatory shock capturing scheme using flux limited dissipation

A method for modifying the third order dissipative terms by the introduction of flux limiters is proposed. The first order dissipative terms can then be eliminated entirely, and in the case of a scalar conservation law the scheme is converted into a total variation diminishing scheme provided that an appropriate value is chosen for the dissipative coefficient. Particular attention is given to: (1) the treatment of the scalar conservation law; (2) the treatment of the Euler equations for inviscid compressible flow; (3) the boundary conditions; and (4) multistage time stepping and multigrid schemes. Numerical results for transonic flows suggest that a central difference scheme augmented by flux limited dissipative terms can lead to an effective nonoscillatory shock capturing method.