Comparing ModelC, ModelD, And ModelW

Selecting the correct model type is one of the most important formulation choices in Exasim. It controls the packed solution layout, the meaning of q, and which initialization data are required.

Feature	ModelC	ModelD	ModelW
q variable	No	Yes	Yes
Auxiliary PDE	None	\(q+\nabla u=0\)	\(\partial q/\partial t+\nabla u=0\)
Diffusion support	Indirect / user-defined	Natural	Possible but not the primary purpose
Wave propagation	Limited	Possible through reformulation	Primary use
Time evolution of q	No	No	Yes
Primary application	Convection / first-order systems	Diffusion / mixed systems	Wave systems
Preprocessing state size	nc = ncu	nc = ncu * (nd + 1)	nc = ncu * (nd + 1)
Backend flags	wave = 0	wave = 0	wave = 1, tdep = 1

Decision Tree

flowchart TD
  A["Does the physical model require a time-evolved q block?"] -->|Yes| W["Use ModelW"]
  A -->|No| B["Do fluxes or sources require gradients of u?"]
  B -->|Yes| D["Use ModelD"]
  B -->|No| C["Use ModelC"]

Practical Guidance

• Start with ModelC for pure transport or inviscid conservation laws.
• Move to ModelD when gradients, diffusion, viscosity, conductivity, or HDG mixed variables are needed.
• Use ModelW only when the auxiliary block is physically time evolved.
• Add w, v, EOS, and AV only when the physics requires those extensions.