On the accuracy of finite-difference solutions for nonlinear water waves

Bingham, Harry B.; Zhang, Haiwen

doi:10.1007/s10665-006-9108-4

Cited by 110 publications

(150 citation statements)

References 29 publications

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“…When depth or nonlinearity increases more resolution is required. Similar tests were carried out for a flexible-order finite difference model in [2]. An immediate conclusion is that the SEM has similar resolution requirements as the corresponding finite difference solver to match the order of accuracy for nonlinear applications.…”

Section: On Nonlinear Accuracy Stability and Kinematics Propertiesmentioning

confidence: 75%

A stabilised nodal spectral element method for fully nonlinear water waves

Engsig-Karup

Eskilsson

Bigoni

2016

Journal of Computational Physics

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We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed and irregular dispersive wave propagation. The benefit of using a high-order -possibly adapted -spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications.1

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Section: On Nonlinear Accuracy Stability and Kinematics Propertiesmentioning

confidence: 75%

A stabilised nodal spectral element method for fully nonlinear water waves

Engsig-Karup

Eskilsson

Bigoni

2016

Journal of Computational Physics

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“…For complete analysis and experimental validation of the algorithm and the involved iterative strategy, we refer to [4,5,20]. The discretization approach based on a flexible-order finite difference method and is briefly summarized in the following for the setup of a NWT.…”

Section: Numerical Methods For Discretizationmentioning

confidence: 99%

“…The analysis of the finite difference model by [4,20] demonstrates that N´ 5-10 points in the vertical are sufficient to achieve satisfactory engineering accuracy levels of, say, less than two percent in wave dispersion and kinematics for typical simulations in costal engineering. This implies that, for typical simulations, the block systems of the form (11) that arise in Zebra-Line smoothing operations will be small.…”

Section: Algorithm 1 Defect Correction Methods For Approximate Solutiomentioning

confidence: 99%

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

Engsig-Karup

Madsen

Glimberg

2011

Numerical Methods in Fluids

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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.

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“…Yan and Liu [29] developed the p-FFT high-order BEM to study nonlinear wave-body interaction problems. Bingham and Zhang [5] used a higher-order finite difference method (FDM) to model nonlinear water waves using potential flow theory. Shao and Faltinsen [22] proposed a potential flow solver, the 2D harmonic polynomial cell (HPC) method, with an order greater than third order.…”

Section: Introductionmentioning

confidence: 99%

Application of a 2D harmonic polynomial cell (HPC) method to singular flows and lifting problems

Liang

Faltinsen

Shao

2015

Applied Ocean Research

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Abstract:Further developments and applications of the 2D harmonic polynomial cell (HPC) method proposed by Shao and Faltinsen [22] are presented. First, a local potential flow solution coupled with the HPC method and based on the domain decomposition strategy is proposed to cope with singular potential flow characteristics at sharp corners fully submerged in a fluid. The results are verified by comparing them with the analytical added mass of a double-wedge in infinite fluid. The effect of the singular potential flow is not dominant for added mass and damping, but the error is non-negligible when calculating mean wave loads using direct pressure integration. Then, the double-layer nodes technique is used to simulate a thin free shear layer shed from lifting bodies, across which the velocity potential is discontinuous. The results are verified by comparing them with analytical results for steady and unsteady lifting problems of a flat plate in infinite fluid. The latter includes the Wagner problem and the Theodorsen functions. Satisfactory agreement with other numerical results is documented for steady linear flow past a foil and beneath the free surface.

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On the accuracy of finite-difference solutions for nonlinear water waves

Cited by 110 publications

References 29 publications

A stabilised nodal spectral element method for fully nonlinear water waves

A stabilised nodal spectral element method for fully nonlinear water waves

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

Application of a 2D harmonic polynomial cell (HPC) method to singular flows and lifting problems

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