We present a fourth-order accurate, multilevel Maxwell solver, discretized in space with a finite volume approach and advanced in time with the classical fourth-order Runge Kutta method (RK4). Electric fields are decomposed into divergence-free and curl-free parts; we solve for the divergence-free parts of Faraday's Law and the Ampère-Maxwell Law while imposing Gauss' Laws as initial conditions. We employ a damping scheme inspired by the Advanced Weather Research and Forecasting Model to eliminate non-physical waves reflected off of coarse-fine grid boundaries, and Kreiss-Oliger artificial dissipation to remove standing wave instabilities. Surprisingly, artificial dissipation appears to damp the spuriously reflected waves at least as effectively as the atmospheric community's damping scheme.
|Advisor:||Colella, Phillip, Morse, Edward|
|Commitee:||Wurtele, Jonathan, van Bibber, Karl|
|School:||University of California, Berkeley|
|School Location:||United States -- California|
|Source:||DAI-B 75/08(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Nuclear engineering, Electromagnetics|
|Keywords:||Advanced weather research and forecasting model, Finite volume approach, Fourth-order, Maxwell's equations, Mesh refinement solver, Runge kutta method|
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