1998/12/01 by Marsha J. Berger, Marsha Berger, Randall J. LeVeque · 7 citations
Engineering · Earth and Planetary Sciences · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Meteorological Phenomena and Simulations #Gas Dynamics and Kinetic Theory
paper · doi:10.1137/s0036142997315974
. An adaptive mesh refinement algorithm developed for the Euler equations of gas dynamics has been extended to employ high-resolution wave-propagation algorithms in a more general framework. This allows its use on a variety of new problems, including hyperbolic equations not in conservation form, problems with source terms or capacity functions, and logically-rectangular curvilinear grids. This framework requires a modified approach to maintaining consistency and conservation at grid interfaces, which is described in detail. The algorithm is implemented in the amrclaw package, which is freely available. 1 Introduction The multi-dimensional wave-propagation algorithm described in [14] is a "high-resolution" method that is second order accurate on smooth solutions while maintaining sharp discontinuities through the use of slope-limiters. While based on ideas developed for hyperbolic systems of conservation laws q t + f(q) x + g(q) y = 0 in the context of shock capturing, these methods ...