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7.1 Synopsis

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

∂u α ---+ λu + ν∇u + ϵ∇ ⋅(D ∇u ) = f ∂t
(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 + λu = f SteadyDiffusionReaction 2D only Continuous/Discontinuous
ϵ∇2u + V∇u + λu = f SteadyAdvectionDiffusionReaction 2D only Continuous/Discontinuous
∂u ∂t + V∇u = f UnsteadyAdvection All Continuous/Discontinuous
∂u ∂t = ϵ∇2u UnsteadyDiffusion All Continuous/Discontinuous
∂u ∂t = ϵ∇2u + R(u) UnsteadyReactionDiffusion All Continuous
∂u ∂t + V∇u = ϵ∇2u UnsteadyAdvectionDiffusion All Continuous/Discontinuous
∂u ∂t + u∇u = 0 UnsteadyInviscidBurger 1D only Continuous/Discontinuous

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

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