DG Wave Element, General Form

Using this element to create an element optimized for solving wave equation using the discontinuous Galerkin method. The section settings for the DG Wave Element, General Form node () are similar to the ones for the General Form Equation node, with the following exceptions:

Coefficients

Use the Type list to select the type of the equation: Normal (the default) and Interior boundary source. The latter option can only be used in boundary conditions. Also note that boundary conditions do not support the Γ and da coefficients. Those settings are disabled for the Interior boundary source type; otherwise they are simply ignored when the equation is used on a boundary.

For this element, the conservative flux Γ, the source term f, and the damping or mass coefficient da are applicable.

Dependent Variable

The Variable names field supports a comma-separated list of dependent variable names. It is important that you enter multiple dependent variables in the same order for all element nodes. Multiple dependent variables are necessary to allow cross-coupling in the da and Γ coefficients. All dependent variables must use the nodal discontinuous Lagrange shape function. For multiple dependent variables, the value of N in the Coefficients section is the sum of all lengths of the dependent variables.

Advanced

Always enter numerical values in the Lax-Friedrichs flux parameter field with the length N, the sum of all lengths of the dependent variables.

To include filter coefficients, select the Activate filter check box. The filter coefficients — α, η, and s — can be NaN (not-a-number, which is the default value) to disable that filter coefficient. Each filter coefficient expects a scalar value.

Axial symmetry is not automatically handled by the equation form. The coefficients have to be reformulated to include gradients and volume factors for axial symmetry.