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On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 219 (4 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Numerical Solution Of Problems On Unbounded Domains. A Review
 A review, Appl. Numer. Math
, 1998
"... While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears most significant in many ..."
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Cited by 126 (19 self)
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While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems represent a wide class of important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms and interpretation of the results. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computa...
NonReflecting Inflow and Outflow in Wind Tunnel for Transonic TimeAccurate Simulation
 J. Math. Anal. Appl
, 1997
"... this paper, we consider a flow problem in an infinitely long wind tunnel. We write out nonlocal artificial boundary conditions, transparent boundary conditions (TBCs), for inflow and outflow boundaries of the computational domain. For this purpose we use timedependent Euler equations linearized ar ..."
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Cited by 10 (2 self)
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this paper, we consider a flow problem in an infinitely long wind tunnel. We write out nonlocal artificial boundary conditions, transparent boundary conditions (TBCs), for inflow and outflow boundaries of the computational domain. For this purpose we use timedependent Euler equations linearized around the uniform freestream flow. Exact transfer of conditions from left infinity to an inflow crosssection of the wind tunnel, and from right infinity to an outflow crosssection is made. These TBCs can be applied for the simulation of unsteady flows with homogeneous initial and boundary conditions outside the computational domain, e.g. for problems with separations, aeroelastic problems, flatter problems etc. However such flows should not have, of course, strong vorticity and strong entropy change in the wake; otherwise the linearized equations used here can lead to the loss of accuracy because perturbations of the longitudinal velocity component and density do not vanish downstream. Clearly, the nonlocal TBCs obtained below require large computational efforts for numerical implementation compared with wellknown characteristicbased boundary conditions. Nevertheless, at least the three following arguments justify the use of TBCs in numerical algorithms. First, they provide the confidence that a problem with TBCs in a bounded (computational) domain substitutes equivalently for the input problem in an unbounded domain (by supposing that a flow in the truncated part of space is described by the linearized Euler equations. In this sense, the conditions are exact). Secondly, by the nature, TBCs permit the use of comparatively small computational domains to simulate external unsteady problems. Note that for the latter, in contrast to the steadystate case, one can not enlarg...
Artificial Boundary Conditions for Computation of Oscillating External Flows
, 1996
"... In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be cau ..."
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Cited by 8 (6 self)
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In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be caused by the timeperiodic injection of fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To conduct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boundary and to further consider only a finite computational domain. Consequently, we will need to formulate some artificial boundary conditions (ABC's) at the introduced external boundary. The ABC's we are aiming to obtain must meet a fundamental requirement. One should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exteri...
Artificial Boundary Conditions Based On The Difference Potentials Method
 IN PROCEEDINGS OF THE SIXTH INTERNATIONAL SYMPOSIUM ON COMPUTATIONAL FLUID DYNAMICS, IV
, 1996
"... While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant i ..."
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Cited by 6 (3 self)
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While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensiv...
NonRe ecting Boundary Conditions for Euler Equation Calculations
 AIAA Paper
, 1989
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Exact nonreflecting boundary conditions revisited: wellposedness and stability
"... Exact nonreflecting boundary conditions for an incompletely parabolic system have been studied. It is shown that wellposedness is a fundamental property of the nonreflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementa ..."
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Exact nonreflecting boundary conditions for an incompletely parabolic system have been studied. It is shown that wellposedness is a fundamental property of the nonreflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, energy stability follows automatically. The stability in combination with the high order accuracy results in a reliable, efficient and accurate method. The theory is supported by numerical simulations. 1