Algebraic multigrid for a mass-consistent wind model, the Nordic Urban Dispersion model

Abstract: In preparation for, and for decision support during, CBRN (chemical, biological, radiological and nuclear) emergencies it is essential to know how such an event would turn out, so that one can prepare a possible evacuation. Afterwards it might be good to know how to backtrack and see what caused the emergency, and in the case of e.g. a gas leak, where did it begin? The Swedish Defence Research Agency (FOI) develops models for such scenarios. In this thesis FOI's model, "The Nordic Urban Dispersion model" (NUD), has been studied. The system of equations set up by this model was originally solved using Intel's PARDISO solver, which is a direct solver. An evaluation on how an iterative multigrid method would work to solve the system has been done in this thesis. The wind model is a mass-consistent model which sets up a diagnostic initial wind field. The final wind field is later minimized under the constraint of the continuity equation. The minimization problem is solved using Lagrange multipliers and the system turns into a Poisson-like problem. The iterative algebraic multigrid solver (AMG) which has been evaluated had difficulties solving the problem of an asymmetric system matrix generated by NUD. The AMG solver was then tried on a symmetric discrete Poisson problem instead, and the solution turns out to be the same as for the PARDISO solver. A comparison was made between the AMG and PARDISO solver, and for the discrete Poisson case the AMG solver turned out on top for both larger system size and less computational time. To try out the solvers for the original NUD case a modification of the boundary conditions was made to make the system matrix symmetric. This modification turns the problem into a mathematical problem rather than a physical one, as the wind fields generated are not physically correct. For this modified case both the solvers get the same solution in essentially the same computational time. A method of how to in the future solve the original (asymmetric) problem, by modifying the discretization of the boundary conditions, has been discussed.