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Center for Nonlinear Studies |
An understanding of the movement of water near and on the shore yields valuable insight into coastal erosion, accretion, groundwater flow, and flood protection. It has proven difficult, however, to model coastal water flow while maintaining efficiency, qualitative correctness and an accurate assessment of the shoreline position. We have developed an algorithm with several components which attempts to overcome these difficulties. We have used a Lax-Wendroff/Lax-Friedrichs hybrid finite volume method, have incorporated a moving mesh into our integrator, and, most importantly, have employed a Lagrangian reference frame in order to handle the crucial task of tracking the shoreline position. While this algorithm is still in development, I will explain and demonstrate how this algorithm is currently applied, its strengths, and its current problems.