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7.1 Synopsis

The ADRSolver is designed to solve partial differential equations of the form:

∂u α∂t-+ λu + V ⋅∇u + f = ϵ∇ ⋅(D ∇u )+ R (u)
(7.1)

in either discontinuous or continuous projections of the solution field. For a full list of the equations which are supported, and the capabilities of each equation, see the table below.

Equation to solve EquationType Dimensions Projections
u = f Projection All Continuous/Discontinuous
∇2u = 0 Laplace All Continuous/Discontinuous
∇2u = f Poisson All Continuous/Discontinuous
∇2u -λu = f Helmholtz All Continuous/Discontinuous
ϵ∇2u -V ⋅∇u = f SteadyAdvectionDiffusion 2D only Continuous/Discontinuous
ϵ∇2u -V ⋅∇u + λu = f SteadyAdvectionDiffusionReaction 2D only Continuous/Discontinuous
∂∂ut + V ⋅∇u = 0 UnsteadyAdvection All Continuous/Discontinuous
∂u ∂t + V ⋅∇u = ϵ∇2u UnsteadyAdvectionDiffusion All Continuous/Discontinuous
∂u ∂t = ϵ∇⋅(D∇u) UnsteadyDiffusion All Continuous/Discontinuous
∂u ∂t = ϵ∇⋅(D∇u) + R(u) UnsteadyReactionDiffusion All Continuous/Discontinuous
∂u ∂t + u∇u = 0 UnsteadyInviscidBurgers 1D only Continuous/Discontinuous
∂u ∂t + u∇u = ϵ∇2u UnsteadyViscousBurgers 1D only Continuous/Discontinuous

Table 7.1: Equations supported by the ADRSolver with their capabilities.

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