Quad Model Tab

The Quad Model Tab allows for setting the parameters that define a system of conservation laws with quadratic flux functions.

The model parameters are specified in "Quad Settings". The general flux functions are \(\(f(u, v) = a_1 u^2/2 + b_1 u v + c_1 v^2/2 + d_1 u + e_1 v,\)\) \(\(g(u, v) = a_2 u^2/2 + b_2 u v + c_2 v^2/2 + d_2 u + e_2 v.\)\)

Alternatively, you can specify a model with a bounded elliptic region in Schaeffer-Shearer normal form in "Duke Flux Params". The flux functions are \(\(f(u, v) = a u^2/2 + b u v + v^2/2 + c v,\)\) \(\(g(u, v) = b u^2/2 + u v - c u.\)\)

You can also specify a model with an unbounded elliptic region with a different normal form in "Unbounded Flux Params". The flux functions are \(\(f(u, v) = a u^2/2 + b u v + v^2/2 + c v,\)\) \(\(g(u, v) = -b u^2/2 - u v + 3 b v^2/2 + c u.\)\)

After choosing flux parameters, you can compute an "optimal" speed range by clicking on "Optimize Speed Range". This speed range is an interval that includes the minimum and maximum values of the characteristic speeds over the domain and has "nice" endpoints.

The four components of the constant viscosity matrix are specified in "Viscosity Params Settings".