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.

scholarly journals Numerical Stability Investigations of the Method of Fundamental Solutions Applied to Wave-Current Interactions Using Generating-Absorbing Boundary Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1153
Author(s):  
Mohammed Loukili ◽  
Denys Dutykh ◽  
Kamila Kotrasova ◽  
Dezhi Ning
Keyword(s):  
Boundary Conditions ◽  
Fundamental Solutions ◽  
Absorbing Boundary Conditions ◽  
Method Of Fundamental Solutions ◽  
Use Case ◽  
Numerical Wave Tank ◽  
Absorbing Boundary ◽  
Numerical Wave ◽  
The Stability ◽  
Water Depths

In this paper, the goal is to revolve around discussing the stability of the Method of Fundamental Solutions (MFS) for the use case of wave-current interactions. Further, the reliability of Generating-Absorbing Boundary Conditions (GABCs) applied to the wave-current interactions is investigated using the Method of Fundamental Solutions (MFS), in a Numerical Wave Tank (NWT) within the potential theory where the main regular manifestations are the periodicity, and symmetry of traveling waves. Besides, the investigations cover different aspects of currents (coplanar current, without current, and opposing current), and also different water depths. Furthermore, the accuracy and stability of the numerical method (MFS) used in this work is evaluated for different locations and numbers of source points.

Time-varying boundary conditions in simulation of seismic wave propagation

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. A1-A6 ◽  
Author(s):  
Robin P. Fletcher ◽  
Johan O. Robertsson
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Waveform Inversion ◽  
Seismic Wave Propagation ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Reverse Time ◽  
Time Migration

We propose two new boundary conditions to regulate coherent reflections from the model boundaries in numerical solutions of wave equations. Both boundary conditions have the common feature that the boundary condition is varied with respect to time. The first boundary condition expands or contracts the computational model during a modeling simulation. The effect is to cause a Doppler shift in the reflected wavefield that can be used to shift energy outside a frequency band of interest. In addition, when the computational domain is expanding, the range of possible incidence angles on the boundary is restricted. This can be used to increase the effectiveness of many existing absorbing boundary conditions that are more effective for incidence angles close to normal. The second boundary condition is an extension of random boundaries. By carefully changing the realization of a random boundary over time, a more diffusive wavefield can be simulated. We show results with 2D numerical simulations of the scalar wave equation for both these boundary conditions. The first boundary condition has application to modeling, but both these boundary conditions have potential application within algorithms that rely upon modeling kernels, such as reverse-time migration and full-waveform inversion.

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.

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.

Absorbing boundary conditions for acoustic media

Geophysics ◽  
1985 ◽  
Vol 50 (6) ◽  
pp. 892-902 ◽  
Author(s):  
R. G. Keys
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Plane Waves ◽  
Basic Element ◽  
Absorbing Boundary Conditions ◽  
Boundary Operator ◽  
Order Differential Operator ◽  
Absorbing Boundary ◽  
Boundary Operators

By decomposing the acoustic wave equation into incoming and outgoing components, an absorbing boundary condition can be derived to eliminate reflections from plane waves according to their direction of propagation. This boundary condition is characterized by a first‐order differential operator. The differential operator, or absorbing boundary operator, is the basic element from which more complicated boundary conditions can be constructed. The absorbing boundary operator can be designed to absorb perfectly plane waves traveling in any two directions. By combining two or more absorption operators, boundary conditions can be created which absorb plane waves propagating in any number of directions. Absorbing boundary operators simplify the task of designing boundary conditions to reduce the detrimental effects of outgoing waves in many wave propagation problems.

An optimal absorbing boundary condition for elastic wave modeling

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 296-301 ◽  
Author(s):  
Chengbin Peng ◽  
M. Nafi Toksöz
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Short Note ◽  
Absorbing Boundary Conditions ◽  
Parallel Computer ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary

Absorbing boundary conditions are widely used in numerical modeling of wave propagation in unbounded media to reduce reflections from artificial boundaries (Lindman, 1975; Clayton and Engquist, 1977; Reynolds, 1978; Liao et al., 1984; Cerjan et al., 1985; Randall, 1988; Higdon, 1991). We are interested in a particular absorbing boundary condition that has maximum absorbing ability with a minimum amount of computation and storage. This is practical for 3-D simulation of elastic wave propagation by a finite‐difference method. Peng and Toksöz (1994) developed a method to design a class of optimal absorbing boundary conditions for a given operator length. In this short note, we give a brief introduction to this technique, and we compare the optimal absorbing boundary conditions against those by Reynolds (1978) and Higdon (1991) using examples of 3-D elastic finite‐difference modeling on an nCUBE-2 parallel computer. In the Appendix, we also give explicit formulas for computing coefficients of the optimal absorbing boundary conditions.

Generating and Absorbing Boundary Conditions for Free-Surface Flow Simulations in Offshore Applications

2015 ◽  
Author(s):  
Bülent Düz ◽  
René H. M. Huijsmans ◽  
Peter R. Wellens ◽  
Mart J. A. Borsboom ◽  
Arthur E. P. Veldman ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Cfd Simulation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Wave Impact ◽  
Absorbing Boundary ◽  
Floating Structures ◽  
Hydrodynamic Wave

Numerical simulations of wave phenomena necessarily have to be carried out in a limited computational domain. This implies that incoming waves should be prescribed properly, and the outgoing waves should leave the domain without causing reflections. In this paper we will present an enhanced type of such generating and absorbing boundary conditions (GABC). The new approach is applied in studies of extreme hydrodynamic wave impact on rigid and floating structures in offshore and coastal engineering, for which the VOF-based CFD simulation tool ComFLOW has been developed.

scholarly journals Performance advantages of CPML over UPML absorbing boundary conditions in FDTD algorithm

2017 ◽  
Vol 68 (1) ◽  
pp. 47-53 ◽  
Author(s):  
Branko D. Gvozdic ◽  
Dusan Z. Djurdjevic
Keyword(s):  
Boundary Conditions ◽  
Electromagnetic Waves ◽  
Fdtd Method ◽  
Absorbing Boundary Conditions ◽  
Numerical Code ◽  
Computational Domain ◽  
Absorbing Boundary ◽  
Simulation Performance ◽  
Efficient Type ◽  
Computer Resources

Abstract Implementation of absorbing boundary condition (ABC) has a very important role in simulation performance and accuracy in finite difference time domain (FDTD) method. The perfectly matched layer (PML) is the most efficient type of ABC. The aim of this paper is to give detailed insight in and discussion of boundary conditions and hence to simplify the choice of PML used for termination of computational domain in FDTD method. In particular, we demonstrate that using the convolutional PML (CPML) has significant advantages in terms of implementation in FDTD method and reducing computer resources than using uniaxial PML (UPML). An extensive number of numerical experiments has been performed and results have shown that CPML is more efficient in electromagnetic waves absorption. Numerical code is prepared, several problems are analyzed and relative error is calculated and presented.

Sign in / Sign up

Export Citation Format

Share Document