SUPERLINEAR CONSERVATION LAW WITH VISCOSITY

The Conservation Law

On vanishing viscosity approximation of conservation laws with discontinuous flux

This note is devoted to a characterization of the vanishing viscosity limit for multi-dimensional conservation laws of the form ut + div f(x, u) = 0, u|t=0 = u0 in the domain R × R . The flux f = f(x, u) is assumed locally Lipschitz continuous in the unknown u and piecewise constant in the space variable x; the discontinuities of f(·, u) are contained in the union of a locally finite number of ...

A fast simulation method with arbitrary viscosity law

A new approach to DSMC collision modelling, called viscosity-DSMC or μ-DSMC, is described in which the time-averaged temperature is used to set the characteristic collision cross-section in each cell such that the Chapman-Enskog viscosity is that given by any desired viscosity law μ = μ (T ), including a curve fit to experimental data. For example, a hard sphere collision model, with hard spher...

Vanishing Viscosity Approximation to Hyperbolic Conservation Laws

We study high order convergence of vanishing viscosity approximation to scalar hyperbolic conservation laws in one space dimension. We prove that, under suitable assumptions, in the region where the solution is smooth, the viscous solution admits an expansion in powers of the viscosity parameter ε. This allows an extrapolation procedure that yields high order approximation to the non-viscous li...

Adaptive Spectral Viscosity for Hyperbolic Conservation Laws

Spectral approximations to nonlinear hyperbolic conservation laws require dissipative regularization for stability. The dissipative mechanism must on the other hand be small enough, in order to retain the spectral accuracy in regions where the solution is smooth. We introduce a new form of viscous regularization which is activated only in the local neighborhood of shock discontinuities. The bas...