Results 1  10
of
14
A New Discrete Transparent Boundary Condition for Standard and Wide Angle "Parabolic" Equations in Underwater Acoustics
"... This paper is concerned with transparent boundary conditions (TBCs) for standard and wide angle “parabolic” equations (SPE, WAPE) in the application to underwater acoustics (assuming cylindrical symmetry). Existing discretizations of these TBCs have accuracy problems and render the overall Crank–Nic ..."
Abstract

Cited by 48 (16 self)
 Add to MetaCart
(Show Context)
This paper is concerned with transparent boundary conditions (TBCs) for standard and wide angle “parabolic” equations (SPE, WAPE) in the application to underwater acoustics (assuming cylindrical symmetry). Existing discretizations of these TBCs have accuracy problems and render the overall Crank–Nicolson finite difference method only conditionally stable. Here, a novel discrete TBC is derived from the discrete whole–space problem that yields an unconditionally stable scheme. The superiority of the new discrete TBC over existing discretizations is illustrated on several benchmark problems.
A supergridscale model for simulating compressible flow on unbounded domains
 J. Comput. Phys
, 2002
"... A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
(Show Context)
A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to develop a model to damp flow disturbances (advective and acoustic) that propagate outside an arbitrarily defined near field. This effectively simulates a freespace boundary condition. Damping the solution in the far field is accomplished in a simple and effective way by applying a filter (similar to that used in largeeddy simulation) on a mesh in Fourier space, followed by a secondary filtering of the equations on the physical grid and implementation of a model for the unresolved scales. The final form of the buffer region is given in real space, independent of any discretization of the equations. Here we use a dealiased, Fourier spectral collocation method to demonstrate the efficacy of the buffer region for several model problems: acoustic wave propagation, convection of a finiteamplitude vortex, and a viscous starting jet in two dimensions. The results compare favorably to previous nonreflecting and absorbing boundary conditions. c © 2002 Elsevier Science (USA)
Nonreflecting boundary conditions based on nonlinear multidimensional characteristics
, 2007
"... Nonlinear characteristic boundary conditions based on multidimensional wave modeling are proposed for two and threedimensional full compressible NavierStokes equations with/without scalar transport equations. This model is consistent with the physics of flows and transport properties. Based on th ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Nonlinear characteristic boundary conditions based on multidimensional wave modeling are proposed for two and threedimensional full compressible NavierStokes equations with/without scalar transport equations. This model is consistent with the physics of flows and transport properties. Based on the theory of characteristics, the multidimensional flows can be decomposed into acoustic, entropy, and vorticity waves. In order to obtain appropriate nonreflecting boundary conditions, the corresponding characteristic variables of incoming waves are set to zeros, and the source terms of the incoming acoustic wave are partially damped. The plane waves are analyzed to obtain the optimal damping coefficient. This new approach substantially minimizes the spurious wave reflections of pressure, density, temperature, and velocity as well as vorticity from the artificial boundaries, where strong multidimensional flow effects exist. The proposed method has advantages of simplicity, robustness, and numerical accuracy, due to the fact that it conforms to the flow physics. The multidimensional characteristicsbased nonreflecting boundary conditions are tested on two benchmark problems: cylindrical acoustic waves propagation and the wake flow after cylinder with periodic strong vortex convected out of the computational domain. These numerical simulations yield accurate results and verify that the method substantially improve the onedimensional characteristicsbased nonreflecting boundary conditions for the complex multidimensional flows. Key words: nonreflecting boundary conditions; nonlinear multidimensional characteristics; complex multidimensional flows; compressible NavierStokes equations; LODI; spurious wave reflection. ∗ Corresponding author.
Finite Difference Schemes on unbounded Domains
"... We discuss the nonstandard problem of using the finite difference method to solve numerically a partial differential equation posed on an unbounded domain. We propose different strategies to construct so–called discrete artificial boundary conditions (ABCs) and present an efficient implementation by ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
We discuss the nonstandard problem of using the finite difference method to solve numerically a partial differential equation posed on an unbounded domain. We propose different strategies to construct so–called discrete artificial boundary conditions (ABCs) and present an efficient implementation by the sum–of–exponential ansatz. The derivation of the ABCs is based on the knowledge of the exact solution, the construction of asymptotic solutions or the usage of a continued fraction expansion to a second–order difference equation. Our approach is explained by means of three different types of partial differential equations arising in option pricing, in quantum mechanics and in (underwater) acoustics. Finally, we conclude with an illustrating numerical example from underwater acoustics showing the superiority of our new approach. 1
A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in (1+1)D
, 2013
"... A finite difference scheme is presented for the Dirac equation in (1+1)D. It can handle space and timedependent mass and potential terms and utilizes exact discrete transparent boundary conditions (DTBCs). Based on a space and timestaggered leapfrog scheme it avoids fermion doubling and preserv ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
A finite difference scheme is presented for the Dirac equation in (1+1)D. It can handle space and timedependent mass and potential terms and utilizes exact discrete transparent boundary conditions (DTBCs). Based on a space and timestaggered leapfrog scheme it avoids fermion doubling and preserves the dispersion relation of the continuum problem for mass zero (Weyl equation) exactly. Considering boundary regions, each with a constant mass and potential term, the associated DTBCs are derived by first applying this finite difference scheme and then using the Ztransform in the discrete time variable. The resulting constant coefficient difference equation in space can be solved exactly on each of the two semiinfinite exterior domains. Admitting only solutions in l2 which vanish at infinity is equivalent to imposing outgoing boundary conditions. An inverse Ztransformation leads to exact DTBCs in form of a convolution in discrete time which suppress spurious reflections at the boundaries and enforce stability of the whole spacetime scheme. An exactly preserved functional for the norm of the Dirac spinor on the staggered grid is presented. Simulations of Gaussian wave packets, leaving the computational domain without reflection, demonstrate the quality of the DTBCs numerically, as well as the importance of a faithful representation of the energymomentum dispersion relation on a grid.
Computation Of Sound Generation And Flow/acoustic Instabilities In The Flow Past An Open Cavity
, 1999
"... The modes of oscillation and radiated acoustic fields of compressible flows over open cavities are investigated computationally. The compressible NavierStokes equations are solved directly (no turbulence model) for two dimensional open cavities with laminar boundary layers upstream. The computation ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The modes of oscillation and radiated acoustic fields of compressible flows over open cavities are investigated computationally. The compressible NavierStokes equations are solved directly (no turbulence model) for two dimensional open cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field. The results show a bifurcation from a shear layer mode, for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear layer mode is well characterized by Rossiter modes and these oscillations lead to intense upstream acoustic radiation dominated by a single frequency. The wake mode is characterized instead by a largescale vortex shedding with Strouhal number nearly independent the Mach number. The vortex shedding causes the boundary layer to periodically separate upstream of the cavity. Acoustic radiation is more intense, with multiple frequencies present. The wake mode oscillation is similar to that reported by Gharib & Roshko (1987) for incompressible cavity flows with laminar upstream boundary layers.
An Integrated Modeling and Simulation Approach for FlowGenerated Sound Prediction
, 2007
"... ..."
(Show Context)
1.2. Mass continuity 1 1.3. Momentum equation 1 1.4. Energy equation 2
"... numerical considerations ..."
(Show Context)
unknown title
, 2003
"... boundarynormal flux gradients works better than imposing vanishing fluxes but neither is entirely satisfactory. 2003 Elsevier B.V. All rights reserved. several different approaches to boundary conditions for the hyperbolic Euler system of equations, (see [1–3] for reviews). Since many of these app ..."
Abstract
 Add to MetaCart
(Show Context)
boundarynormal flux gradients works better than imposing vanishing fluxes but neither is entirely satisfactory. 2003 Elsevier B.V. All rights reserved. several different approaches to boundary conditions for the hyperbolic Euler system of equations, (see [1–3] for reviews). Since many of these approaches are designed for use in computational aeroacoustics, they set high standards for the amount of reflection acceptable at outflow boundaries [4]. For viscous, multicomponent, reacting flow fields governed by the (incompletely parabolic) Navier–
Non Reflecting Boundary Conditions For Reacting Flows
"... In this paper we explore the specification of time dependent boundary conditions suitable for the simulation of low Mach number reacting flows. The standard treatments used to date are based on the method of characteristics, and essentially set to zero the incoming characteristics; this practise ha ..."
Abstract
 Add to MetaCart
In this paper we explore the specification of time dependent boundary conditions suitable for the simulation of low Mach number reacting flows. The standard treatments used to date are based on the method of characteristics, and essentially set to zero the incoming characteristics; this practise has been shown to have deleterious effects on the flow evolution. The new approach, while still based on the method of characteristics, circumvents this problem through the application of a double expansion in terms of an appropriately defined Mach number. In the method, a low Mach number expansion of the dependent variables is coupled to a twolength scale decomposition. Through the double expansion, it is possible to separate inertial events (i.e. those moving at the local convection velocity) from acoustic events (those moving at the local sound speed). The paper highlights why previous treatments have encountered difficulties in turbulent flows, and provides a method by which heat release effects can be incorporated into a nonreflecting boundary condition framework. The accuracy of the method is demonstrated using a curved stagnating flame, in which the reaction zone crosses the boundary. 1