The Wave Form PDE (wahw) interface (), found under the Mathematics>PDE Interfaces branch () when adding an interface, solves wave equations formulated with first order derivatives in time and space using the discontinuous Galerkin method and is highly optimized with respect to speed and memory consumption.

When you add this interface, these default nodes are also added to the Model Builder: Wave Form PDE, Zero Flux, and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions. You can also right-click Wave Form PDE to select features from the context menu.

Use the wave form for first-order hyperbolic PDEs. Assuming a scalar equation for the dependent variable u, these problems take the form

The terms da, Γ, f, and g are coefficients. They can be functions of both the spatial coordinates or time, and the solution u, but not the derivatives of u. The coefficients f and g are scalar, whereas Γ is the flux vector. The coefficient da is assumed to be nonzero throughout the domain Ω, and for all times.

The Label is the default physics interface name.

The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.

The default Name (for the first Wave Form PDE interface in the model) is wahw.

Select the Dependent variable quantity that defines the unit for the dependent variable u. The default is Dimensionless (with 1 in the Unit column). Click the Select Dependent Variable Quantity button () to open the Physical Quantity dialog box to browse to find a physical quantity to use. You can also type a search string in the text field at the top of the dialog box and then click the Filter button () to filter the list of physical quantities. For example, type potential and click the Filter button to only list physical quantities that represent some kind of potential. Alternatively, click the Define Dependent Variable Unit button () to edit the unit directly in the Unit column, typing a unit to define the dependent variable quantity. The quantity column then contains Custom unit.

Select the Source term quantity that defines the unit for the source term f (the unit for the right — and left — side of the PDE). Custom unit is the default quantity (with m^-2 in the Unit column). Click the Select Source Term Quantity button () to open the Physical Quantity dialog box to browse to find a physical quantity to use. You can also type a search string in the text field at the top of the dialog box and then click the Filter button () to filter the list of physical quantities. For example, type potential and click the Filter button to only list physical quantities that represent some kind of potential. Alternatively, click the Define Source Term Unit button () to edit the unit directly in the Unit column, typing a unit (for example, W/m^3 or A/m^3) to define the dependent variable quantity. The quantity column then contains Custom unit.

Due to efficiency reasons, there is only one Shape function type (finite element type) defined for this interface — the Nodal discontinuous Lagrange functions. The associated element order (the order of the shape function for the element) can be chosen from the Element order list. The highest available order is 10 in 1D and 2D models and 7 in 3D models, and the default order is two.

To display additional settings in this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.

Define the number of the dependent variables and the variable names. The default name for a scalar PDE variable is u.

Enter the Number of dependent variables. Use the Add dependent variable () and Remove dependent variable () buttons as needed.