Boundary conditions on a finite grid: Applications with pseudospectral wave propagation

Geophysics ◽  
1997 ◽  
Vol 62 (5) ◽  
pp. 1544-1557 ◽  
Author(s):  
Huatao Wu ◽  
Jonathan M. Lees
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Optimal Parameter ◽  
Two Dimensions ◽  
New Method ◽  
Head Waves ◽  
Vertical Fault ◽  
Reduction Function ◽  
Grid Nodes

A new method for calculating boundary conditions at the free surface and along absorbing boundaries of a finite grid is presented. A finite, twice differentiable reduction function that achieves a 99% reduction over three wavelengths is proposed and tested. In the context of pseudospectral wave propagation, this implies a boundary layer of at least six grid nodes. The method is analyzed in one and two dimensions and the problems of waves impinging on corners are addressed. The reduction function recommended is [Formula: see text] where α is a parameter to be determined by optimization. Tests of the performance of the new method versus other common schemes are presented and analyzed. We provide a strategy for determining the optimal parameter in the reduction function. Synthetic Rayleigh waves are observed at the free surface of the simulation. Experiments with a vertical fault plane show the presence of direct, reflected, transmitted, and head waves. The presence of head waves may be used to analyze velocity contrasts across fault zones.

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.

Reflection of coupled dilatational and shear waves in the generalized micropolar thermoelastic materials

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1948-1955 ◽  
Author(s):  
Rengsi Lianngenga ◽  
Sanasam S Singh
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Shear Wave ◽  
Shear Waves ◽  
Energy Ratios ◽  
Micropolar Thermoelasticity ◽  
Incident Waves

The problem of wave propagation in the generalized theory of micropolar thermoelasticity under the Green–Lindsay model has been investigated. We have investigated the reflected dilatational and shear waves due to incident waves at a plane-free surface of generalized micropolar thermoelastic materials. The amplitude and energy ratios corresponding to the reflected coupled dilatational and coupled shear waves are derived using boundary conditions at the free surface. These ratios are also computed numerically for a particular model. Note that there are critical angles for the incident shear wave.

scholarly journals A Numerical Method for Predicting Acoustical Wave Propagation in Open Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Johnny Papageorgakopoulos ◽  
Sokrates Tsangaris
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Near Field ◽  
Sound Field ◽  
Vortex Pair ◽  
Rectangular Domain ◽  
Two Dimensions ◽  
Curvilinear Coordinates ◽  
Benchmark Problems ◽  
Computational Domain

We present a numerical methodology for evaluating wave propagation phenomena in two dimensions in the time domain with focus on the linear acoustic second-order wave equation. An outline of the higher-order compact discretization schemes followed by the time discretization technique is first presented. The method is completed with the addition of spatial filtering based on the same compact schemes' principles. The important role of boundary conditions is subsequently addressed. Two popular ways to truncate the computational domain in the near field are presented and compared here: first the formulation of “absorbing conditions” in the form of partial differential equations especially for the origin and second the construction of an absorbing layer surrounding the domain, in which waves (after they have exited the domain) are attenuated and decayed exponentially. Subsequently, the method is assessed by recalling three benchmark problems. In the first where a Gaussian pulse is generated and propagated in a 2D rectangular domain, the accuracy and absorbability of the boundary conditions are compared. In the second, a similar situation is investigated but under curvilinear coordinates and under the presence of a solid body which scatters the pulse. Finally the sound field inducted by the flow of corotating vortex pair is calculated and compared with the corresponding analytical solution.

2-D MULTIPLE REFLECTIONS

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 592-620 ◽  
Author(s):  
Don C. Riley ◽  
Jon F. Claerbout
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Dimensions ◽  
Acoustic Medium ◽  
Multiple Reflections ◽  
Surface Reflection ◽  
Forward Calculation ◽  
Initial Boundary Value

Starting with a 1-D subsurface model, a method is developed for modeling and inverting the class of multiple reflections involving the near‐perfect reflector at the free surface. A solution to the practical problem of estimating the source waveform is discussed, and application of the 1-D algorithm to field data illustrates the successful elimination of seafloor and peg‐leg multiples. Extending the analysis to waves in two dimensions, we make the approximation that the subsurface behaves as an acoustic medium. Based on several numerical and theoretical considerations, the scalar wave equation is split into two separate partial differential equations: one governing propagation of upcoming waves and a second describing downgoing waves. The result is a pair of propagation equations which are coupled where reflectors exist. Finite difference approximations to the initial boundary value problem are developed to integrate numerically the surface reflection seismogram. Use of the 2‐D algorithm for modeling free‐surface multiple reflections is illustrated by several reflector models. The 2-D inverse problem of simultaneously migrating primary reflections and inverting diffracted multiples consists of reversing the forward calculation with the data as boundary conditions. Causal directions of propagation are related to downward continuation of surface data. Reflector mapping principles are used to develop a general reflection coefficient estimator. The inverse algorithm is illustrated using the results of the 2-D forward calculation as the boundary conditions.

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

scholarly journals Influence of Boundary Conditions in Numerical Simulation of Free Surface Vortices

2015 ◽  
Vol 82 ◽  
pp. 893-899 ◽  
Author(s):  
Luca Cristofano ◽  
Matteo Nobili
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Boundary Conditions

Boundaries Influence on the Flow Field Around an Oscillating Sphere

2013 ◽  
Author(s):  
Domenica Mirauda ◽  
Antonio Volpe Plantamura ◽  
Stefano Malavasi
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Boundary Conditions ◽  
Damping Ratio ◽  
Water Channel ◽  
Open Water ◽  
Free Surface Flows ◽  
The Body ◽  
Sphere Diameter ◽  
Oscillating Sphere

This work analyzes the effects of the interaction between an oscillating sphere and free surface flows through the reconstruction of the flow field around the body and the analysis of the displacements. The experiments were performed in an open water channel, where the sphere had three different boundary conditions in respect to the flow, defined as h* (the ratio between the distance of the sphere upper surface from the free surface and the sphere diameter). A quasi-symmetric condition at h* = 2, with the sphere equally distant from the free surface and the channel bottom, and two conditions of asymmetric bounded flow, one with the sphere located at a distance of 0.003m from the bottom at h* = 3.97 and the other with the sphere close to the free surface at h* = 0, were considered. The sphere was free to move in two directions, streamwise (x) and transverse to the flow (y), and was characterized by values of mass ratio, m* = 1.34 (ratio between the system mass and the displaced fluid mass), and damping ratio, ζ = 0.004. The comparison between the results of the analyzed boundary conditions has shown the strong influence of the free surface on the evolution of the vortex structures downstream the obstacle.

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