Multiresolution schemes for conservation laws with viscosity
The author presents multiresolution schemes for the efficient numerical solution of one-dimensional conservation laws with viscosity. The method computes the cell average multiresolution representation of the solution which provides much information about the solution's regularity. Hence, the possible extensive essentially nonoscillatory (ENO) reconstruction as well as flux computations are performed only near discontinuities. The multiresolution scheme is also expected to `follow' possibly unsteady irregularities from one time step to the next. When viscosity is added, predicting the location of the regularity becomes a problem of estimating the change in shock thickness. Therefore, shock width estimates are derived for the 1D prototype equations.
expensive essentially nonoscillatory reconstruction
scientific article; zbMATH DE number 851764
scientific article