Solving thermoviscous acoustic problems can easily involve solving for many degrees of freedom (DOFs) as the model solves for the acoustic variations in both pressure, velocity field (2 or 3 components), and temperature. First of all, it is important to restrict the use of the thermoviscous acoustics model to domains and regions of the model where it is necessary. Couple to Pressure Acoustics using the multiphysics coupling. In the frequency domain use the Narrow Region Acoustics feature or the Thermoviscous Boundary Layer Impedance feature of Pressure Acoustics to reduce the number of DOFs. Secondly, care should be taken when meshing the computational domain. If these two things have been carefully considered, the solver can be changed from its default Direct setting to use an Iterative solver suggestion. Depending on the model size and involved physics two options are described below.

In both cases, a good starting point for setting up a new solver configuration is to right-click the study node and select Show Default Solver, then expand the Solver Configuration tree under Stationary Solver or Time-Dependent Solver. Predefined iterative solver suggestions are automatically generated. Per default, a direct solver is used and two iterative solvers are suggested and disabled. To turn on one of these approaches, right-click the solver and select Enable (or press F4).

Both suggestions are described below as well as how to set them up manually (in most cases the default suggestions should be used). In liquids where thermal effects can be neglected, the model can be solved in the Adiabatic formulation and DOFs saved. Choosing different shape functions can also reduce the memory consumption, for example, switching to serendipity elements. Finally, the default P1-P2-P2 discretization can be changed to an all linear discretization if Stabilization is enabled.

For large 2D problems and 3D problems, that only involve thermoviscous acoustics, using the following approach will save around 20% memory and can speed up the solution procedure by a factor 2 or 3. Under the Stationary Solver node take the following steps: Add an Iterative solver with the GMRES solver. As preconditioner add the Direct Preconditioner and switch the solver to PARDISO. Expand the Hybridization section and select Multi preconditioner in the Preconditioner variables list add the Pressure and Velocity field. Add a second direct preconditioner with the same settings but now select only the Temperature as preconditioner variables. Set the Pivoting Perturbation to 1e-13 for the pressure-velocity group. The reason for splitting the equations up in this manner is that the energy equation is only loosely coupled to the momentum and continuity equations.

Start by adding an Iterative solver and select GMRES as the solver. Then right-click the iterative node and select Domain Decomposition (Schwartz). A good starting point for this solver, is to use the default settings with only a few changes:

This type of approach should allow you to solve large thermoviscous acoustics models, also including multiphysics interactions, using a minimum of RAM. Possibly increase the value of the Maximum number of DOFs per subdomain option to use a larger amount of the RAM at your disposition.

This is achieved by selecting the Adiabatic formulation option under the Thermoviscous Acoustics Equation Settings section. When Adiabatic formulation is selected, all temperature options and conditions are disabled in the user interface.

In models with a structured mesh, it can be advantageous to switch to the serendipity shape functions instead of the default Lagrange, see Lagrange and Serendipity Shape Functions below. In general, if a boundary layer mesh is used (to resolve the thermal and viscous boundary layers) or if a PML is used in the model, the mesh contains structured mesh regions.