Automatic Generation of Higher-order Finite Volume Embedded Boundary Discretizations

Hans Johansen, Lawrence Berkeley National Laboratory
December 4th, 2013 at 3:30PM–4:30PM in 939 Evans Hall [Map]

We present an embedded boundary approach to finite-volume discretizations that is based on “cut cell” representations. Using geometric moments of arbitrarily high order, we assemble small linear systems that express local consistency of the finite volume flux stencils, and directly affect stability and other properties of the resulting operators. One difficulty with these types of methods is the presence of arbitrarily small cells; typical approaches give up on conservation, merge or rotate cells, or modify the domain to avoid stability issues (such as severe explicit time step restrictions). For our approach, we can show how to treat arbitrarily-small cells, so that the discrete flux-divergence operator retains its higher-order accuracy and desired spectrum. This also allows us to avoid finicky grid generation, maintain conservation properties, and handle variable coefficient problems. The flexibility and accuracy of the approach is demonstrated for model problems in 1D and in 2D domains, with straightforward extension to 3D and moving boundaries.