7.3 Session file configuration

The type of equation which is to be solved is specified through the EquationType SOLVERINFO option in the session file. This can be set as in table 7.1. At present, the Steady non-symmetric solvers cannot be used in parallel.

7.3.1 Time Integration Scheme

• TimeIntegrationScheme: The following types of time integration schemes have been tested with each solver:

  EqType	Explicit	Diagonally Implicit	IMEX	Implicit
  UnsteadyAdvection	✓
  UnsteadyDiffusion	✓	✓
  UnsteadyReactionDiffusion			✓
  UnsteadyAdvectionDiffusion			✓
  UnsteadyInviscidBurger	✓

7.3.2 Solver Info

The solver info are listed below:

• Eqtype: This sets the type of equation to solve, according to the table above.
• Projection: The Galerkin projection used may be either:
  • Continuous for a C0-continuous Galerkin (CG) projection.
  • Discontinuous for a discontinous Galerkin (DG) projection.
• DiffusionAdvancement: This specifies how to treat the diffusion term. This will be restricted by the choice of time integration scheme:
  • Explicit Requires the use of an explicit time integration scheme.
  • Implicit Requires the use of a diagonally implicit, IMEX or Implicit scheme.
• AdvectionAdvancement: This specifies how to treat the advection term. This will be restricted by the choice of time integration scheme:
  • Explicit Requires the use of an explicit or IMEX time integration scheme.
  • Implicit Not supported at present.
• AdvectionType: Specifies the type of advection:
  • NonConservative (for CG only).
  • WeakDG (for DG only).
• DiffusionType:
  • LDG (The penalty term is proportional to an optional parameter LDGc11 which is by default set to one; proportionality to polynomial order can be manually imposed by setting the parameter LDGc11 equal to p²).
• UpwindType:
  • Upwind.

7.3.3 Parameters

The following parameters can be specified in the PARAMETERS section of the session file:

• epsilon: sets the diffusion coefficient ϵ.
  Can be used in: SteadyDiffusionReaction, SteadyAdvectionDiffusionReaction, UnsteadyDiffusion, UnsteadyAdvectionDiffusion.
  Default value: 0.
• d00, d11, d22: sets the diagonal entries of the diffusion tensor D.
  Can be used in: UnsteadyDiffusion
  Default value: All set to 1 (i.e. identity matrix).
• lambda: sets the reaction coefficient λ.
  Can be used in: SteadyDiffusionReaction, Helmholtz, SteadyAdvectionDiffusionReaction
  Default value: 0.

7.3.4 Functions

The following functions can be specified inside the CONDITIONS section of the session file:

• AdvectionVelocity: specifies the advection velocity V.
• InitialConditions: specifies the initial condition for unsteady problems.
• Forcing: specifies the forcing function f.