High-Order Phase-Resolving Method for Wave Transformation Over Natural Shorelines

Abstract

Abstract The use of nature-based facilities has become a popular solution to coastal hazard mitigation and shoreline stabilization. Emergent vegetation, such as mangrove forests, has been proven an effective protective system for alleviating wave and surge impact during a tsunami or tropical cyclone event. To reduce the quantification work and uncertain parameterized equations when modeling the wave height attenuation and momentum dissipation through emergent marsh vegetation, a new approach for implementing a high order Cut Finite Element Method (CutFEM) for problems with embedded solid structures in viscous incompressible flows is presented. The CutFEM allows using the same number of degrees of freedom as the underlying conforming Galerkin method on the fixed background mesh, which is independent of the configuration of non-conforming interfaces. Therefore, it has the same element assembly structure as classical FEM on the background mesh. No explicit generation of cut cell meshes, adaptive quadrature, or local refinement is required. The idea of equivalent polynomials is also adopted to compute the exact integration involving products of polynomials with Heaviside and Dirac distributions. Therefore, this method gains high-order accuracy for embedded interfaces and robustness of the signed distance representation in the level set field. The numerical method that uses a physical model of mock-up mangrove forests is validated through the wave flume experiment conducted by Kelty et al. at OSU. The correlations between the numerical results and experimental measurements are presented. All numerical simulations are completed by the open-source toolkit Proteus.