Scalar Model Tab

The Scalar Model Tab offers tools for specifying parameters for a pair of conservation laws for which each flux depends solely on its own variable; thus the two equations decouple, i.e., the model is effectively two scalar conservation laws in the two coordinate directions. Specifically, the model equations are

u_t + f(u)_x = eps_u u_xx,
v_t + g(v)_x = eps_v v_xx

where

f(u) = a sin(2 pi alpha u) + b sin(2 pi beta u)

with a, alpha, b, and beta being constants, and

g(v) = .5 k (v - v0)^2

(giving Burgers equation) with the constants k and v0 being such that the characteristic speeds Df(u) and Dg(v) are distinct for all u and v in the interval [-1, 1].

Model parameters are specified on "ConsLaw Settings Tab"; the viscosity matrix parameters are specified on "Viscosity Matrix Settings Tab"; and the domain in which the unknowns vary is specified on "Domain WorkArea Settings Tab".