Multiscale evaluation method of the drag effect on shallow water flow through coastal forests based on 3D numerical simulations

Abstract

This study presents a method for determining the drag parameter in the 2D shallow water (SW) equation for flows through a coastal forest by conducting a series of 3D numerical simulations (3D NSs). Following the theory of multiscale modeling, an evaluation method procedure is proposed. We first prepare a local test domain that contains a sufficient number of trees to constitute part of a coastal forest. Then, 3D NSs are conducted in this test domain with various inflow conditions. Based on the corresponding results, the momentum losses over the test domain are converted into the drag parameter of the global SW equation. A response surface of the drag parameter is constructed as a function of the flow conditions. The stabilized finite element method is employed for both the local and the global NSs, and the phase-field method is utilized to represent 3D free surfaces. Comparisons between the 2D SW calculation results and the 3D NS results are also performed to verify the validity of the proposed method.

On the flow conditions requiring detailed geometric modeling for multiscale evaluation of coastal forests

“…This section is devoted to describing the multiscale evaluation method for assessing the disaster mitigation performance of trees that was recently proposed in our previous work [30]. In line with the previous setting, the spatial scale for numerical flow tests (NFTs) in this study is also set to be consistent with the model experiment conducted by Hayashi et al 2015[36] using miniature trees for validation purposes.…”

“…The flow condition around trees at the real scale is associated with that of miniature models using the Froude number as established in our previous study [30]. Specifically, the Froude number of the inflow in our NFTs as well as the model experiment [36] is assumed to be the same as that of the actual scale flow, so that the following condition is satisfied:…”

“…In the context of multiscale modeling, we assume that the macroscopic flow characteristics (Figure 1 a) can be evaluated by performing the spatial averaging of the flow characteristics in a representative domain on the local or, equivalently, microscopic scale, which is illustrated in Figure 1 b. In other words, the method proposed in the previous study [30] hinges on NFTs to be conducted in the "local test domain (LTD)" that contains arrays of the detailed tree or circular cylinder models. The idea of NFTs with an LTD underlies the theory of spatial averaging based on the scale separation principle as commonly assumed in computational homogenization; see [37,38,39].…”

“…It should be noted here that the regularized pressure loss in Eq. ( 14) is considered a key macroscopic factor in our previous multiscale evaluation of coastal forests [30].…”

“…To answer the question posed above, in this paper, the multiscale evaluation method [30] is applied to assess the impact of different geometric models of trees on their macroscopic attenuation effects against tsunami-like flow. Specifically, by arranging simple cylinder and detailed tree models in an open channel that mimics a coastal forest, we conduct a series of NFTs, i.e., 3D flow simulations in the LTD, under various inflow conditions with different inflow velocities and depths to evaluate the macroscopic attenuation property and discuss the effect of the canopies of the tree model.…”