A Comparison of Dirichlet and Neumann Wavemakers for the Numerical Generation and Propagation of Nonlinear Long-Crested Surface Waves

2003 ◽  
Author(s):  
R. E. Baddour ◽  
W. Parsons
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Surface Boundary ◽  
Homogeneous Fluid ◽  
Surface Boundary Conditions ◽  
Lateral Boundary Conditions ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Numerical Generation ◽  
Finite Extent

We are studying numerically the problem of generation and propagation of gravity long-crested waves in a tank containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent and of infinite depth. A non-orthogonal curvilinear coordinate system, which follows the free surface is constructed and the full nonlinear kinematic and dynamic free surface boundary conditions are utilized in the algorithm. “Wavemakers” are modeled using both the Dirichlet and Neumann lateral boundary conditions and a full comparison is given.

A Comparison of Dirichlet and Neumann Wavemakers for the Numerical Generation and Propagation of Nonlinear Long-Crested Surface Waves

2004 ◽  
Vol 126 (4) ◽  
pp. 287-296
Author(s):  
R. E. Baddour ◽  
W. Parsons
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Surface Boundary ◽  
Good Resolution ◽  
Homogeneous Fluid ◽  
Surface Boundary Conditions ◽  
Lateral Boundary Conditions ◽  
Curvilinear Coordinate ◽  
Numerical Generation ◽  
Neumann Model

We are studying numerically the problem of generation and propagation of long-crested gravity waves in a tank containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent and of infinite depth. A nonorthogonal curvilinear coordinate system, which follows the free surface, is constructed and the full nonlinear kinematic and dynamic free surface boundary conditions are utilized in the algorithm. “Wavemakers” are modeled using both the Dirichlet and Neumann lateral boundary conditions and a full comparison is given. Overall, the Dirichlet model was more stable than the Neumann model, with an upper limit steepness S=2A/λ of 0.08 using good resolution compared with the Neumann’s maximum of 0.05.

Studies in the Stability of a Numerical Wave Tank Model for Generation and Propagation of Steep Nonlinear Long-Crested Surface Waves

2005 ◽  
Author(s):  
W. Parsons ◽  
R. E. Baddour
Keyword(s):  
Free Surface ◽  
Continuity Condition ◽  
Surface Boundary ◽  
Homogeneous Fluid ◽  
Surface Boundary Conditions ◽  
Curvilinear Coordinate ◽  
Underlying Causes ◽  
Steep Waves ◽  
The Stability ◽  
Numerical Beach

We are studying numerically the problem of generation and propagation of gravity long-crested waves in a tank containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent and of infinite depth. A non-orthogonal curvilinear coordinate system, which follows the free surface is constructed which gives a realistic “continuity condition”, since it tracks the entire fluid domain at all times. A depth profile of the potential is assumed, and employed to perform a waveform relaxation algorithm to decouple the discrete Laplacian along dimensional lines, thereby reducing it’s computation over this total fluid domain. In addition, the full nonlinear kinematic and dynamic free surface boundary conditions are utilized in the algorithm, and a suitably tuned numerical beach is used to avoid reflections. It is well known that instability, in the form of generated spurious “sawtooth waves”, plagues this problem, leading to numerical overflow. This makes it very difficult to generate steep waves for sufficiently long simulation times. The authors have struggled with this problem for some time, with significant success, by employing an “aliasing filter”. This paper outlines our ongoing study of the stability of the model, including an analysis of the possible nature of the underlying causes including compatibility conditions. We conclude by giving a simple practical technique for greatly improving the stability.

Novel free surface boundary conditions for spilling breaking waves

2020 ◽  
Vol 159 ◽  
pp. 103717
Author(s):  
Nikta Iravani ◽  
Peyman Badiei ◽  
Maurizio Brocchini
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Breaking Waves ◽  
Surface Boundary ◽  
Surface Boundary Conditions

REEF3D::FNPF: A Flexible Fully Nonlinear Potential Flow Solver

2019 ◽  
Author(s):  
Hans Bihs ◽  
Weizhi Wang ◽  
Tobias Martin ◽  
Arun Kamath
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Surface Boundary ◽  
Flow Solver ◽  
Surface Boundary Conditions ◽  
Nonlinear Potential ◽  
Numerical Wave ◽  
Computational Resources

Abstract In situations where the calculation of ocean wave propagation and impact on offshore structures is required, fast numerical solvers are desired in order to find relevant wave events in a first step. After the identification of the relevant events, Computational Fluid Dynamics (CFD) based Numerical Wave Tanks (NWT) with an interface capturing two-phase flow approach can be used to resolve the complex wave structure interaction, including breaking wave kinematics. CFD models emphasize detail of the hydrodynamic physics, which makes them not the ideal candidate for the event identification due to the large computational resources involved. In the current paper a new numerical wave model is represented that solves the Laplace equation for the flow potential and the nonlinear kinematic and dynamics free surface boundary conditions. This approach requires reduced computational resources compared to CFD based NWTs. In contrast to existing approaches, the resulting fully nonlinear potential flow solver REEF3D::FNPF uses a σ-coordinate grid for the computations. Solid boundaries are incorporated through a ghost cell immersed boundary method. The free surface boundary conditions are discretized using fifth-order WENO finite difference methods and the third-order TVD Runge-Kutta scheme for time stepping. The Laplace equation for the potential is solved with Hypres stabilized bi-conjugated gradient solver preconditioned with geometric multi-grid. REEF3D::FNPF is fully parallelized following the domain decomposition strategy and the MPI communication protocol. The model is successfully tested for wave propagation benchmark cases for shallow water conditions with variable bottom as well as deep water.

Fully Nonlinear Energy Flux Calculations for Long-Crested Surface Waves

2006 ◽  
Author(s):  
W. Parsons ◽  
R. E. Baddour
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Energy Flux ◽  
Bottom Topography ◽  
Finite Depth ◽  
Surface Boundary ◽  
Homogeneous Fluid ◽  
Fully Nonlinear ◽  
Surface Boundary Conditions ◽  
Type Boundary

We employ a fully nonlinear numerical model to generate and propagate long-crested gravity waves in a tank containing an incompressible invicid homogeneous fluid, initially at rest, with a horizontal free surface of finite extent and of finite depth. A non-orthogonal curvilinear coordinate system is constructed which follows the free surface and is “fitted” to the bottom topography of the tank and therefore tracks the entire fluid domain at all times. A waveform relaxation algorithm provides an efficient iterative method to solve the resulting discrete Laplace equation, and the full nonlinear kinematic and dynamic free surface boundary conditions are employed to propagate the solution. In addition, a monochromatic deterministic theoretical wave-maker, employing a Dirichlet type boundary condition, and a suitably tuned numerical beach are utilized in the numerical model. We first show that the model generates the appropriate dispersion relation for both the deep water and shallow water conditions. Subsequently, we calculate the energy and energy flux for small steepness waves and show that the model produces the expected linear results. We complete the paper by considering steeper waves where the linear results are suspect.

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