A new fully non‐hydrostatic 3D free surface flow model for water wave motions

Ai, Congfang; Jin, Shaohua; Lv, Biao

doi:10.1002/fld.2317

Cited by 57 publications

(43 citation statements)

References 28 publications

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“…This method enabled the pressure condition at the free surface to be exactly assigned to zero without any approximation. Badiei et al (2008) and Ai et al (2011) presented non-hydrostatic finite volume models based on a vertical boundary fitted grid system. The vertical boundary fitted grid system has been chosen as the computational mesh, which enables the model to simulate free surface flows over irregular geometries.…”

Section: Introductionmentioning

confidence: 99%

A higher-efficient three-dimensional numerical model for small amplitude free surface flows

2014

China Ocean Eng

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A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers.

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Section: Introductionmentioning

confidence: 99%

A higher-efficient three-dimensional numerical model for small amplitude free surface flows

2014

China Ocean Eng

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“…The obtained algebraic system of equations in is well conditioned when the sign rules and are applied. Its solution does not require the application of any complicated and bulky Bi‐CGSTAB Krylov methods with Incomplete LU‐factotization (ILU) or GMRES method . Simple iteration is enough:

Δ P_{i}^{italicm + 1} = {‖boldC‖}^{- 1} \times ((), F^{'} - (‖‖, A) \times Δ P_{italici - 1}^{m} - (‖‖, B) \times Δ P_{italici + 1}^{m}) .

…”

Section: Iterative Methods Of Solving the Discrete Form Of The Poissonmentioning

confidence: 99%

“…The same applies to obtaining the equation for pressure correction in case of equation splitting (Section 2). Such an approach has often been applied when using σ coordinates, as well as with other vertical discretizations . Potential problems and limitations are the following: The main problem is not obtaining but solving the discrete form of the Poisson equation: The iteration methods usually converge poorly and take most of the calculation time.…”

Section: Problem Statementmentioning

confidence: 99%

“…This makes it necessary to apply complex iteration procedures: in Stelling and Zijlema and Zijlema and Stelling, variants of the biconjugate gradient stabilized (Bi‐CGSTAB) Krylov method are recommended for a multilayer model. In Ai et al, a preconditioned conjugate gradient method is used. In Ullmann, the efficiency of the Bi‐CGSTAB and generalized minimal residual methods (GMRES) is compared.…”

Section: Problem Statementmentioning

confidence: 99%

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Multilayer open flow model: A simple pressure correction method for wave problems

Prokof'ev

2017

Numerical Methods in Fluids

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Summary This paper describes a pressure correction method for single‐ and multilayer open flow models. The method does not require any complex procedures to solve the discretization of the Poisson equation and is distinguished by a high computational efficiency. The algorithm can easily be adapted to irregular meshes and parallelized. Parabolic interpolation of the pressure profile is used for the free surface. The discretization of the Poisson equation is written in a matrix form, allowing its usage also in the case of basic function expansion of the depth pressure profile. The paper presents the results of algorithm verification where experimental data sensitive to the numerical dissipation of the calculation model was used. Iteration convergence is high including problems with dry‐bed flooding. The complete described technique of pressure correction is implemented in OpenCL on the GPU. Computation time for a test problem solved using CPU and GPU is compared.

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“…[21] The standing wave in a closed basin of constant depth was calculated to assess the discrete dispersive relation of the present model [e.g., Walters, 2005;Ai et al, 2010]. The initial wave height that causes a standing wave with a wavelength l was given as = A cos(2px/l) at t = 0 where A is the amplitude.…”

Section: Standing Wave In Closed Basinmentioning

confidence: 99%

Three‐dimensional tsunami propagation simulations using an unstructured mesh finite element model

et al. 2013

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[1] Large-scale tsunami propagation simulations from the fault region to the coast are conducted using a three-dimensional (3-D) parallel unstructured mesh finite element code (Fluidity-ICOM). Unlike conventional 2-D approximation models, our tsunami model solves the full 3-D incompressible Navier-Stokes (NS) equations. The model is tested against analytical solutions to simple dispersive wave propagation problems. Comparisons of our 3-D NS model results with those from linear shallow water and linear dispersive wave models demonstrate that the 3-D NS model simulates the dispersion of very short wavelength components more accurately than the 2-D models. This improved accuracy is achieved using only a small number (three to five) of vertical layers in the mesh. The numerical error in the wave velocity compared with the linear wave theory is less than 3% up to kH = 40, where k is the wave number and H is the sea depth. The same 2-D and 3-D models are also used to simulate two earthquake-generated tsunamis off the coast of Japan: the 2004 off Kii peninsula and the 2011 off Tohoku tsunamis. The linear dispersive and NS models showed good agreement in the leading waves but differed especially in their near-source, short wavelength dispersive wave components. This is consistent with the results from earlier tests, suggesting that the 3-D NS simulations are more accurate. The computational performance on a parallel computer showed good scalability up to 512 cores. By using a combination of unstructured meshes and high-performance computers, highly accurate 3-D tsunami simulations can be conducted in a practical timescale.Citation: Oishi, Y., M. D. Piggott, T. Maeda, S. C. Kramer, G. S. Collins, H. Tsushima, and T. Furumura (2013), Threedimensional tsunami propagation simulations using an unstructured mesh finite element model,

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A new fully non‐hydrostatic 3D free surface flow model for water wave motions

Cited by 57 publications

References 28 publications

A higher-efficient three-dimensional numerical model for small amplitude free surface flows

A higher-efficient three-dimensional numerical model for small amplitude free surface flows

Multilayer open flow model: A simple pressure correction method for wave problems

Three‐dimensional tsunami propagation simulations using an unstructured mesh finite element model

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