4.1 Synopsis

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

α ∂t-+ λu + ν∇u  + ϵ∇  ⋅(D ∇u ) = f

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
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∇2uV∇u + λu = f SteadyAdvectionDiffusionReaction 2D only Continuous/Discontinuous
∂t + V∇u = f UnsteadyAdvection All Continuous/Discontinuous
∂t = ϵ∇2u UnsteadyDiffusion All Continuous/Discontinuous
∂t + V∇u = ϵ∇2u UnsteadyAdvectionDiffusion All Continuous/Discontinuous
∂t + u∇u = 0 UnsteadyInviscidBurger 1D only Continuous/Discontinuous

Table 4.1: Equations supported by the ADRSolver with their capabilities.