Towards a General-Purpose Open Boundary Condition for Wave Simulations

2011 ◽  
Author(s):  
Bulent Duz ◽  
Rene H. M. Huijsmans ◽  
Peter R. Wellens ◽  
Mart J. A. Borsboom ◽  
Arthur E. P. Veldman
Keyword(s):  
Boundary Condition ◽  
Three Dimensional ◽  
General Purpose ◽  
Absorbing Boundary Conditions ◽  
Design Stage ◽  
Open Boundary ◽  
Computational Domain ◽  
Absorbing Boundary ◽  
Scaled Model ◽  
Artificial Boundaries

For the design of FPSO’s in harsh environments an accurate assessment of the ability of the platform to survive in extreme sea conditions is of prime importance. Next to scaled model tests on the FPSO in waves also CFD capabilities are at the disposal of the designer. However even with the fastest computers available it is still a challenge to use CFD in the design stage because of the large computational resources they require. In that respect to use a small computational domain will improve the turn around time of the computations, however at the expense of various numerical artifacts, like reflection on artificial boundaries in the computational domain. In order to mitigate the reflection properties new absorbing boundary conditions have been developed. The work in this paper is constructed on the previous study about the generating and absorbing boundary condition (GABC) in the ComFLOW project. We present a method to apply the GABC on all the boundaries in a three dimensional domain. The implementation of the GABC in ComFLOW is explained in detail.

Stability of wide‐angle absorbing boundary conditions for the wave equation

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1153-1163 ◽  
Author(s):  
R. A. Renaut ◽  
J. Petersen
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Least Squares ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Wide Angle ◽  
Courant Number ◽  
Absorbing Boundary ◽  
Wide Range ◽  
Artificial Boundaries

Numerical solution of the two‐dimensional wave equation requires mapping from a physical domain without boundaries to a computational domain with artificial boundaries. For realistic solutions, the artificial boundaries should cause waves to pass directly through and thus mimic total absorption of energy. An artificial boundary which propagates waves in one direction only is derived from approximations to the one‐way wave equation and is commonly called an absorbing boundary. Here we investigate order 2 absorbing boundary conditions which include the standard paraxial approximation. Absorption properties are compared analytically and numerically. Our numerical results confirm that the [Formula: see text] or Chebychev‐Padé approximations are best for wide‐angle absorption and that the Chebychev or least‐squares approximations are best for uniform absorption over a wide range of incident angles. Our results also demonstrate, however, that the boundary conditions are stable for varying ranges of Courant number (ratio of time step to grid size). We prove that there is a stability barrier on the Courant number specified by the coefficients of the boundary conditions. Thus, proving stability of the interior scheme is not sufficient. Furthermore, waves may radiate spontaneously from the boundary, causing instability, even if the stability bound on the Courant number is satisfied. Consequently, the Chebychev and least‐squares conditions may be preferred for wide‐angle absorption also.

scholarly journals Equivalent Boundary Conditions for Heterogeneous Acoustic Media

2014 ◽  
Vol 15 (3) ◽  
pp. 301
Author(s):  
Manuela Longoni De Castro ◽  
Julien Diaz ◽  
Victor Perón
Keyword(s):  
Boundary Conditions ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Absorbing Boundary ◽  
Equivalent Boundary ◽  
Artificial Boundaries ◽  
Acoustic Media ◽  
Propagation Of Waves

In this work, we have worked on possibilities to model artificial boundaries needed in the simulation of wave propagation in acoustic heterogeneous media.  Our motivation is to restrict the computational domain in the simulation of seismic waves that are propagated from the earth and transmitted to the stratified heterogeneous media composed by ocean and atmosphere. Two possibilities were studied and compared in computational tests: the use of absorbing boundary conditions on an artificial boundary in the atmosphere layer and the elimination of the atmosphere layer using an equivalent boundary condition that mimics the propagation of waves through the atmosphere. <br />

scholarly journals A Generating - Absorbing Boundary Condition Applied to Wave - Current Interactions Using the Method of Fundamental Solutions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammed Loukili ◽  
Kamila Kotrasova ◽  
Amine Bouaine
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Fundamental Solutions ◽  
Absorbing Boundary Conditions ◽  
Method Of Fundamental Solutions ◽  
Computational Domain ◽  
Numerical Wave Tank ◽  
Absorbing Boundary ◽  
Wave Properties

Abstract The purpose of this work is to study the feasibility and efficiency of Generating Absorbing Boundary Conditions (GABCs), applied to wave-current interactions using the Method of Fundamental Solutions (MFS) as radial basis function, the problem is solved by collocation method. The objective is modeling wave-current interactions phenomena applied in a Numerical Wave Tank (NWT) where the flow is described within the potential theory, using a condition without resorting to the sponge layers on the boundaries. To check the feasibility and efficiency of GABCs presented in this paper, we verify accurately the numerical solutions by comparing the numerical solutions with the analytical ones. Further, we check the accuracy of numerical solutions by trying a different number of nodes. Thereafter, we evaluate the influence of different aspects of current (coplanar current, without current, and opposing current) on the wave properties. As an application, we take into account the generating-absorbing boundary conditions GABCs in a computational domain with a wavy downstream wall to confirm the efficiency of the adopted numerical boundary condition.

Acoustic resonances and trapped modes in pipes and tunnels

2008 ◽  
Vol 605 ◽  
pp. 401-428 ◽  
Author(s):  
STEFAN HEIN ◽  
WERNER KOCH
Keyword(s):  
Cross Sections ◽  
High Speed ◽  
Hard Spheres ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Absorbing Boundary Conditions ◽  
Trapped Modes ◽  
Absorbing Boundary ◽  
Complex Scaling Method ◽  
Acoustic Resonances

Acoustic resonances of simple three-dimensional finite-length structures in an infinitely long cylindrical pipe are investigated numerically by solving an eigenvalue problem. To avoid unphysical reflections at the finite grid boundaries placed in the uniform cross-sections of the pipe, perfectly matched layer absorbing boundary conditions are applied in the form of the complex scaling method of atomic and molecular physics. Examples of the structures investigated are sound-hard spheres, cylinders, cavities and closed side branches. Several truly trapped modes with zero radiation loss are identified for frequencies below the first cutoff frequency of the pipe. Such trapped modes can be excited aerodynamically by coherent vortices if the frequency of the shed vortices is close to a resonant frequency. Furthermore, numerical evidence is presented for the existence of isolated embedded trapped modes for annular cavities above the first cutoff frequency and for closed side branches below the first cutoff frequency. As applications of engineering interest, the acoustic resonances are computed for a ball-type valve and around a simple model of a high-speed train in an infinitely long tunnel.

Nonsplit complex-frequency shifted perfectly matched layer combined with symplectic methods for solving second-order seismic wave equations — Part 1: Method

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. T301-T311 ◽  
Author(s):  
Xiao Ma ◽  
Dinghui Yang ◽  
Xueyuan Huang ◽  
Yanjie Zhou
Keyword(s):  
Boundary Condition ◽  
Seismic Wave ◽  
Wave Equations ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Second Order ◽  
Complex Frequency ◽  
Absorbing Boundary ◽  
Time Layer ◽  
The Time Domain

The absorbing boundary condition plays an important role in seismic wave modeling. The perfectly matched layer (PML) boundary condition has been established as one of the most effective and prevalent absorbing boundary conditions. Among the existing PML-type conditions, the complex frequency shift (CFS) PML attracts considerable attention because it can handle the evanescent and grazing waves better. For solving the resultant CFS-PML equation in the time domain, one effective technique is to apply convolution operations, which forms the so-called convolutional PML (CPML). We have developed the corresponding CPML conditions with nonconstant grid compression parameter, and used its combination algorithms specifically with the symplectic partitioned Runge-Kutta and the nearly analytic SPRK methods for solving second-order seismic wave equations. This involves evaluating second-order spatial derivatives with respect to the complex stretching coordinates at the noninteger time layer. Meanwhile, two kinds of simplification algorithms are proposed to compute the composite convolutions terms contained therein.

LONG-TERM STABILITY ANALYSIS OF ACOUSTIC ABSORBING BOUNDARY CONDITIONS

2013 ◽  
Vol 23 (11) ◽  
pp. 2129-2154 ◽  
Author(s):  
HÉLÈNE BARUCQ ◽  
JULIEN DIAZ ◽  
VÉRONIQUE DUPRAT
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Acoustic Wave Equation ◽  
Absorbing Boundary ◽  
Term Stability ◽  
Long Term Stability ◽  
The Stability

This work deals with the stability analysis of a one-parameter family of Absorbing Boundary Conditions (ABC) that have been derived for the acoustic wave equation. We tackle the problem of long-term stability of the wave field both at the continuous and the numerical levels. We first define a function of energy and show that it is decreasing in time. Its discrete form is also decreasing under a Courant–Friedrichs–Lewy (CFL) condition that does not depend on the ABC. Moreover, the decay rate of the continuous energy can be determined: it is exponential if the computational domain is star-shaped and this property can be illustrated numerically.

An Absorbing Boundary Condition Based on Perfectly Matched Layer Technique Combined with Discontinuous Galerkin Boltzmann Method for Low Mach Number Flow Noise

2018 ◽  
Vol 26 (04) ◽  
pp. 1850011 ◽  
Author(s):  
Weidong Shao ◽  
Jun Li
Keyword(s):  
Boundary Condition ◽  
Discontinuous Galerkin ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Condition ◽  
Time Behavior ◽  
Computational Domain ◽  
Mean Flow ◽  
Absorbing Boundary ◽  
Flow Noise ◽  
Boltzmann Method

For flow noise simulations, the nonreflecting boundary condition (NRBC) is significant to confine the computational domain to a small domain. Lattice Boltzmann method (LBM) has advantages for noise because of its low dissipation, but is limited to the uniform grid. In this paper, an absorbing boundary condition (ABC) based on perfectly matched layer (PML) technique is introduced to LBM. Then PML stability is analyzed and a new strategy is developed to achieve robustness. Invoking the decoupling time integration, the underlying equation for streaming is solved with the nodal discontinuous Galerkin method. Benchmark acoustic problems were used to demonstrate the PML absorption. Moreover, PML parameters, long time behavior and inhomogeneous pseudo mean flow are discussed. The methodology appears to work very well and would be hoped for practical flow noise computation.

Numerical Simulation of Nonlinear Wave Diffraction by a Vertical Cylinder in a Narrow Flume, Wide Tank, and Infinitely Wide Tank

2003 ◽  
Author(s):  
Alaa M. Mansour ◽  
A. Neil Williams
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Nonlinear Wave ◽  
Wave Diffraction ◽  
Open Boundary ◽  
Computational Domain ◽  
Open Boundary Condition ◽  
Lateral Direction ◽  
Cylinder Diameter ◽  
Side Walls

In this paper, a three dimensional numerical wave tank model has been used to simulate fully nonlinear wave diffraction by a uniform vertical circular cylinder. The cylinder has been placed in a narrow flume of a width equal to four times the cylinder diameter. The runup and the hydrodynamic forces on the cylinder has been compared to the results when a similar cylinder is placed in a similar tank but with a width equal to sixteen times the cylinder diameter. The model has been further extended by applying an open boundary condition to the side-walls to simulate an infinitely wide tank and hence more realistically simulate open sea condition. The proposed open boundary condition in the lateral direction is based on coupling of two prescribed boundary conditions, namely, numerical beach and Orlanski boundary conditions. The use of this coupled boundary condition has been found to be very efficient in eliminating any significant wave reflection from the side-walls back into the computational domain.

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