A higher-order non-hydrostatic σ model for simulating non-linear refraction–diffraction of water waves

SUMMARYWe implement and evaluate a massively parallel and scalable algorithm based on a multigrid preconditioned Defect Correction method for the simulation of fully nonlinear free surface flows. The simulations are based on a potential model that describes wave propagation over uneven bottoms in three space dimensions and is useful for fast analysis and prediction purposes in coastal and offshore engineering. A dedicated numerical model based on the proposed algorithm is executed in parallel by utilizing affordable modern special purpose graphics processing unit (GPU). The model is based on a low-storage flexible-order accurate finite difference method that is known to be efficient and scalable on a CPU core (single thread). To achieve parallel performance of the relatively complex numerical model, we investigate a new trend in high-performance computing where many-core GPUs are utilized as high-throughput co-processors to the CPU. We describe and demonstrate how this approach makes it possible to do fast desktop computations for large nonlinear wave problems in numerical wave tanks (NWTs) with close to 50/100 million total grid points in double/single precision with 4 GB global device memory available. A new code base has been developed in C++ and compute unified device architecture C and is found to improve the runtime more than an order in magnitude in double precision arithmetic for the same accuracy over an existing CPU (single thread) Fortran 90 code when executed on a single modern GPU. These significant improvements are achieved by carefully implementing the algorithm to minimize data-transfer and take advantage of the massive multi-threading capability of the GPU device.

Section: Benchmarkingmentioning

confidence: 98%

A massively parallel GPU‐accelerated model for analysis of fully nonlinear free surface waves

Engsig-Karup

Madsen

Glimberg

2011

“…For a given tolerance error of 1%, the two-, three-, and five-layer models are capable of resolving linear wave dispersion up to K h ≈ , 2 , and 5 , respectively. In comparison with several other two-layer (or five-layer) non-hydrostatic models [24][25][26]30] that are sufficient up to K h ≈ 1 (or 4 ∼ 5), the present -based non-hydrostatic model yields better accuracy to predict frequency dispersion, demonstrating the success of the embedded Boussinesq-type-like equations. In addition, similar to the top-layer control method [27], the proposed ATLC method provides a simple implementation rule to determine the thickness of the top-layer, which can be used to resolve spectral wave components in a very deep-water regime without water depth's or wave number's dependence [8,26,31].…”

Section: Linear Progressive Wavementioning

confidence: 79%

“…A set of suitable layer size is critical to accurately resolve surface wave propagation [26,27,30]. A top-down resolving technique suggested by Yuan and Wu [31] can effectively capture linear wave dispersion but the layer size's dependence on waves somehow hinders this method in modeling spectral wave groups.…”

Section: Linear Progressive Wavementioning

confidence: 99%

“…The final step is to obtain an analytical-based pressure profile. Integrating the vertical momentum equation (5) from the half of the top-layer cell N 3 to the free surface = 0, applying the Leibniz's rule, and substituting free-surface kinematic boundary condition (6) and free-surface pressure condition, we obtain the pressure field Instead of directly discretizing the above equation for the top-layer cell [19,22,23,30], we substitute the analytical-based velocity profile of Equations (15a), (15b), and (16) into Equation (17), yielding…”

Section: Boussinesq-type-like Equationsmentioning

confidence: 99%

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A σ‐coordinate non‐hydrostatic model with embedded Boussinesq‐type‐like equations for modeling deep‐water waves

Young

2010

Self Cite

SUMMARYA -coordinate non-hydrostatic model, combined with the embedded Boussinesq-type-like equations, a reference velocity, and an adapted top-layer control, is developed to study the evolution of deep-water waves. The advantage of using the Boussinesq-type-like equations with the reference velocity is to provide an analytical-based non-hydrostatic pressure distribution at the top-layer and to optimize wave dispersion property. The -based non-hydrostatic model naturally tackles the so-called overshooting issue in the case of non-linear steep waves. Efficiency and accuracy of this non-hydrostatic model in terms of wave dispersion and nonlinearity are critically examined. Overall results show that the newly developed model using a few layers is capable of resolving the evolution of non-linear deep-water wave groups.

“…(21) as discussed in Section 3.7). A convergence criterion needs to be defined for (line 7) the algorithm (e.g.…”

Section: Algorithmmentioning

confidence: 99%

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

Engsig-Karup

2014

SUMMARYRobust computational procedures for the solution of non‐hydrostatic, free surface, irrotational and inviscid free‐surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable prediction of free‐surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow equations. We present new detailed fundamental analysis using finite‐amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high‐order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow models. Our study is particularly relevant for fast and efficient simulation of non‐breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization parameters for different PDC strategies, we study systematically limits of accuracy, convergence rate, algorithmic and numerical efficiency and scalability of the most efficient known PDC methods. These strategies are of interest, because they enable generalization of geometric multigrid methods to high‐order accurate discretizations and enable significant improvement in numerical efficiency while incuring minimal storage requirements. We demonstrate robustness using such PDC methods for practical ranges of interest for coastal and maritime engineering, that is, from shallow to deep water, and report details of numerical experiments that can be used for benchmarking purposes. Copyright © 2014 John Wiley & Sons, Ltd.