Waves Run-Up and Overtopping Simulations Using Lagrangian Blocks

Abstract

Wave run-up and overtopping of coastal structures are simulated using Lagrangian Blocks on Eulerian Mesh (LBEM). In the LBEM simulations, the blocks carry the mass and momentum. The movement of the blocks is calculated in a Lagrangian reference frame. The water depth defined by the volume blocks is non-negative. The wave fronts across the wet-and-dry interface are simulated by the block method without interruption by the oscillation problem that has limited the applicability of many existing computational methods. To evaluate the accuracy of the LBEM method in this paper, simulations are carried out for (i) the dam-break waves, (ii) the wave run-up on plane beach, and (iii) the overtopping of solitary waves over levee. The simulations of the dam-break wave have produced excellent agreement with the exact solutions by Ritter [1] and Stoker [2], and the semi-analytical solution by Sakkas and Strelkoff [3,4]. The simulations of the wave run-up on plane beach agree with the experimental data and the nonlinear theory of Synolakis [5]. The simulations of wave overtopping trapezoidal dike agree with the finite-volume simulations of Stansby [6]. The results have demonstrated the accuracy of the LBEM method and the versatility of the method for general wave simulations over variable terrain.