Home About us Contact
|
Home About us Contact | ||
|
|
||
Artificial Boundary Conditions (artificial + boundary_condition)
Selected AbstractsArtificial boundary conditions for viscoelastic flowsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2008Sergueď A. Nazarov Abstract The steady three-dimensional exterior flow of a viscoelastic non-Newtonian fluid is approximated by reducing the corresponding nonlinear elliptic,hyperbolic system to a bounded domain. On the truncation surface with a large radius R, nonlinear, local second-order artificial boundary conditions are constructed and a new concept of an artificial transport equation is introduced. Although the asymptotic structure of solutions at infinity is known, certain attributes cannot be found explicitly so that the artificial boundary conditions must be constructed with incomplete information on asymptotics. To show the existence of a solution to the approximation problem and to estimate the asymptotic precision, a general abstract scheme, adapted to the analysis of coupled systems of elliptic,hyperbolic type, is proposed. The error estimates, obtained in weighted Sobolev norms with arbitrarily large smoothness indices, prove an approximation of order O(R,2+,), with any ,>0. Our approach, in contrast to other papers on artificial boundary conditions, does not use the standard assumptions on compactly supported right-hand side f, leads, in particular, to pointwise estimates and provides error bounds with constants independent of both R and f. Copyright © 2007 John Wiley & Sons, Ltd. [source] Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical typeMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2004A. Nazarov, Sergue Abstract The approximation of solutions to boundary value problems on unbounded domains by those on bounded domains is one of the main applications for artificial boundary conditions. Based on asymptotic analysis, here a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly. Existence and uniqueness of approximating solutions are proved together with asymptotically precise error estimates. One class of important examples includes boundary value problems for anisotropic elasticity and piezoelectricity. Copyright © 2004 John Wiley & Sons, Ltd. [source] The control-theory-based artificial boundary conditions for time-dependent wave guide problems in unbounded domainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2005Tianyun Liu Abstract A method is proposed to obtain the high-performance artificial boundary conditions for solving the time-dependent wave guide problems in an unbounded domain. Using the variable separation method, it is possible to reduce the spatial variables of the wave equation by one. Furthermore, introducing auxiliary functions makes the reduced wave equation a linear first-order ordinary differential system with one control input. Solving the closed-loop control system, a stable and accurate artificial boundary condition is obtained in a rigorous mathematical manner. Numerical examples have demonstrated the effectiveness of the proposed artificial boundary conditions for the time-dependent wave guide problems in unbounded domain. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical accuracy of a Padé-type non-reflecting boundary condition for the finite element solution of acoustic scattering problems at high-frequencyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005R. Kechroud Abstract The present text deals with the numerical solution of two-dimensional high-frequency acoustic scattering problems using a new high-order and asymptotic Padé-type artificial boundary condition. The Padé-type condition is easy-to-implement in a Galerkin least-squares (iterative) finite element solver for arbitrarily convex-shaped boundaries. The method accuracy is investigated for different model problems and for the scattering problem by a submarine-shaped scatterer. As a result, relatively small computational domains, optimized according to the shape of the scatterer, can be considered while yielding accurate computations for high-frequencies. Copyright © 2005 John Wiley & Sons, Ltd. [source] Non-reflecting artificial boundaries for transient scalar wave propagation in a two-dimensional infinite homogeneous layerINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Chongbin Zhao Abstract This paper presents an exact non-reflecting boundary condition for dealing with transient scalar wave propagation problems in a two-dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x ,, and another extends toward x,- ,, the non-reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time-dependent partial differential equation with only one spatial variable, can be further changed into a linear first-order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non-reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non-reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi-infinite media. Copyright © 2003 John Wiley & Sons, Ltd. [source] Towards a transparent boundary condition for compressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2001C. H. Bruneau Abstract A new artificial boundary condition for two-dimensional subsonic flows governed by the compressible Navier,Stokes equations is derived. It is based on the hyperbolic part of the equations, according to the way of propagation of the characteristic waves. A reference flow, as well as a convection velocity, is used to properly discretize the terms corresponding to the entering waves. Numerical tests on various classical model problems, whose solutions are known, and comparisons with other boundary conditions (BCs), show the efficiency of the BC. Direct numerical simulations of more complex flows over a dihedral plate are simulated, without creation of acoustic waves going back in the flow. Copyright © 2001 John Wiley & Sons, Ltd. [source] The control-theory-based artificial boundary conditions for time-dependent wave guide problems in unbounded domainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2005Tianyun Liu Abstract A method is proposed to obtain the high-performance artificial boundary conditions for solving the time-dependent wave guide problems in an unbounded domain. Using the variable separation method, it is possible to reduce the spatial variables of the wave equation by one. Furthermore, introducing auxiliary functions makes the reduced wave equation a linear first-order ordinary differential system with one control input. Solving the closed-loop control system, a stable and accurate artificial boundary condition is obtained in a rigorous mathematical manner. Numerical examples have demonstrated the effectiveness of the proposed artificial boundary conditions for the time-dependent wave guide problems in unbounded domain. Copyright © 2005 John Wiley & Sons, Ltd. [source] Non-reflecting artificial boundaries for transient scalar wave propagation in a two-dimensional infinite homogeneous layerINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Chongbin Zhao Abstract This paper presents an exact non-reflecting boundary condition for dealing with transient scalar wave propagation problems in a two-dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x ,, and another extends toward x,- ,, the non-reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time-dependent partial differential equation with only one spatial variable, can be further changed into a linear first-order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non-reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non-reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi-infinite media. Copyright © 2003 John Wiley & Sons, Ltd. [source] Artificial boundary conditions for viscoelastic flowsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2008Sergueď A. Nazarov Abstract The steady three-dimensional exterior flow of a viscoelastic non-Newtonian fluid is approximated by reducing the corresponding nonlinear elliptic,hyperbolic system to a bounded domain. On the truncation surface with a large radius R, nonlinear, local second-order artificial boundary conditions are constructed and a new concept of an artificial transport equation is introduced. Although the asymptotic structure of solutions at infinity is known, certain attributes cannot be found explicitly so that the artificial boundary conditions must be constructed with incomplete information on asymptotics. To show the existence of a solution to the approximation problem and to estimate the asymptotic precision, a general abstract scheme, adapted to the analysis of coupled systems of elliptic,hyperbolic type, is proposed. The error estimates, obtained in weighted Sobolev norms with arbitrarily large smoothness indices, prove an approximation of order O(R,2+,), with any ,>0. Our approach, in contrast to other papers on artificial boundary conditions, does not use the standard assumptions on compactly supported right-hand side f, leads, in particular, to pointwise estimates and provides error bounds with constants independent of both R and f. Copyright © 2007 John Wiley & Sons, Ltd. [source] Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical typeMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2004A. Nazarov, Sergue Abstract The approximation of solutions to boundary value problems on unbounded domains by those on bounded domains is one of the main applications for artificial boundary conditions. Based on asymptotic analysis, here a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly. Existence and uniqueness of approximating solutions are proved together with asymptotically precise error estimates. One class of important examples includes boundary value problems for anisotropic elasticity and piezoelectricity. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||