Nonreflecting boundary conditions based on nonlinear multidimensional characteristics

Liu, Qianlong; Vasilyev, Oleg V.

doi:10.1002/fld.2011

Cited by 20 publications

(20 citation statements)

References 39 publications

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“…Some authors have improved the standard NSCBC method by accounting differently for the contribution of transverse derivatives and viscous fluxes. Indeed, the complete Navier–Stokes equations, using characteristic variables, can be written

[\begin{matrix} left \\ c^{2} \frac{\partial ρ}{\partial t} - \frac{\partial p}{\partial t} \\ \frac{\partial υ}{\partial t} \\ \frac{\partial w}{\partial t} \\ \frac{\partial p}{\partial t} + ρ c \frac{\partial u}{\partial t} \\ \frac{\partial p}{\partial t} - ρ c \frac{\partial u}{\partial t} \end{matrix}] + [\begin{matrix} left \\ c^{2} {scriptL}_{1} \\ {scriptL}_{2} \\ {scriptL}_{3} \\ ρ c {scriptL}_{4} \\ ρ c {scriptL}_{5} \end{matrix}] + [\begin{matrix} left \\ {scriptT}_{1} \\ {scriptT}_{2} \\ {scriptT}_{3} \\ {scriptT}_{4} \\ {scriptT}_{5} \end{matrix}] + [\begin{matrix} left \\ {scriptD}_{1} \\ {scriptD}_{2} \\ {scriptD}_{3} \\ {scriptD}_{4} \\ {scriptD}_{5} \end{matrix}] = [\begin{matrix} left \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{matrix}],

where

normalT

contains all transverse terms, and

normalD

are the diffusive terms.…”

Section: Navier–stokes Characteristic Boundary Conditionsmentioning

confidence: 99%

“…By following the sign of the eigenvalues (u,u C c and u c), we distinguished the characteristic waves as incoming or outgoing waves. Outgoing waves are computed using interior points and one-sided schemes, whereas the incoming waves must be evaluated using information on the boundary condition and Equation (11). The standard LODI method [3] assumes that the flow crossing the boundary is almost inviscid and one dimensional along the normal direction of the boundary interface (which will correspond to the x-axis), so that the term D can be computed using characteristic wave amplitudes.…”

Section: Standard Navier-stokes Characteristic Boundary Conditionsmentioning

confidence: 99%

“…Some authors [5,9,11] have improved the standard NSCBC method by accounting differently for the contribution of transverse derivatives and viscous fluxes. Indeed, the complete Navier-Stokes equations, using characteristic variables, can be written 2 6 6 6 6 6 6 6 4 c 2 @ @t @p @t @v @t @w @t @p @t C c @u @t @p @t c @u…”

Section: Modified Outflow Characteristic-based Conditionsmentioning

confidence: 99%

“…Poinsot and Lele [3] extended these characteristic methods to the Navier-Stokes equations, assuming that the flow is one dimensional in the normal direction of the boundary: the so-called local one-dimensional inviscid (LODI) equations. They have then been improved to handle strongly multidimensional flows and aeroacoustics problems [2,4,5,[9][10][11], and all resulting methods are used for aeroacoustics problems. Another method commonly used is the perfect matched layer method [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Comparison of outflow boundary conditions for subsonic aeroacoustic simulations

Deniau

Lamarque

et al. 2011

Numerical Methods in Fluids

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[\begin{matrix} left \\ c^{2} \frac{\partial ρ}{\partial t} - \frac{\partial p}{\partial t} \\ \frac{\partial υ}{\partial t} \\ \frac{\partial w}{\partial t} \\ \frac{\partial p}{\partial t} + ρ c \frac{\partial u}{\partial t} \\ \frac{\partial p}{\partial t} - ρ c \frac{\partial u}{\partial t} \end{matrix}] + [\begin{matrix} left \\ c^{2} {scriptL}_{1} \\ {scriptL}_{2} \\ {scriptL}_{3} \\ ρ c {scriptL}_{4} \\ ρ c {scriptL}_{5} \end{matrix}] + [\begin{matrix} left \\ {scriptT}_{1} \\ {scriptT}_{2} \\ {scriptT}_{3} \\ {scriptT}_{4} \\ {scriptT}_{5} \end{matrix}] + [\begin{matrix} left \\ {scriptD}_{1} \\ {scriptD}_{2} \\ {scriptD}_{3} \\ {scriptD}_{4} \\ {scriptD}_{5} \end{matrix}] = [\begin{matrix} left \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{matrix}],

where

normalT

contains all transverse terms, and

normalD

are the diffusive terms.…”

Section: Navier–stokes Characteristic Boundary Conditionsmentioning

confidence: 99%

Section: Standard Navier-stokes Characteristic Boundary Conditionsmentioning

confidence: 99%

Section: Modified Outflow Characteristic-based Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparison of outflow boundary conditions for subsonic aeroacoustic simulations

Deniau

Lamarque

et al. 2011

Numerical Methods in Fluids

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“…However, the use of the Lodato et al BC provides some improvements at edges and corner, but does not fully address the coordinate system issue discussed in this work. In 2009, Liu & Vasilyev [7] state a different multi-dimensional characteristic formulation, that separates and will then treat differently characteristic wave convective terms from others, considered as "source terms". Due to acoustic incoming -i.e.…”

Section: Introductionmentioning

confidence: 99%

Flow streamline based Navier–Stokes Characteristic Boundary Conditions: Modeling for transverse and corner outflows

Albin

D'Angelo

2011

Computers & Fluids

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Some limitations of three dimensional Navier-Stokes Characteristic Boundary Conditions (3D-NSCBC) are discussed for flows traveling in a direction that is oblique to the boundary. To limit errors generated at boundaries with flows having any arbitrary direction, it is proposed to organize the wave decomposition in a coordinate system that is attached to the local flow streamline crossing the boundary, because some modeled expressions are not frame independent. Compared to previous 3D-NSCBC, the modified strategy accounting for oblique waves is found to improve the outflow treatment for transverse outgoing vortices, up to vortices crossing an outflow corner. The method is also applied to an expanding laminar flame.

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Cross‐impact of beam local wavenumbers on the efficiency of self‐adaptive artificial boundary conditions for two‐dimensional nonlinear Schrödinger equation

Trofimov

Loginova

Egorenkov

et al. 2023

Math Methods in App Sciences

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In this paper, we propose self‐adaptive artificial boundary conditions (ABCs) for the two‐dimensional (2D) time‐dependent nonlinear Schrödinger equation and studied their efficiency. This equation describes the laser pulse interaction with a semiconductor layer under laser‐induced plasma generation. Because of its nonlinearity, the interaction process is very sensitive to the appearance of the optical beam spurious reflection; therefore, highly transparent ABCs are urgently required to avoid disturbing the interaction process by an unphysical reflected wave. This can be achieved by using time‐ and spatial‐dependent local wavenumbers computed near the artificial boundaries. We claim that it is necessary to account for both wavenumbers in each of the adaptive ABCs stated on both spatial coordinates. Based on computer simulation, we demonstrate an increase in the efficiency of the adaptive ABC stated on the coordinate along which the optical pulse propagates by involving both local wavenumbers. The accuracy of the developed approach is verified using a well‐known analytical solution of the linear Schrödinger equation as well as the reference problem solution, obtained by solving the problem with zero‐value boundary conditions on the extended spatial domain. For computer modeling, the finite‐difference scheme, possessing asymptotic stability, is applied together with a two‐stage iterative process for its realization. The algorithm and peculiarities of the local wavenumber computation are discussed in detail. The applicability of the developed approach is also demonstrated via the solution of both linear and nonlinear problems. The proposed method has widespread application for solving various laser physics problems governed by the Schrödinger equation.

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Nonreflecting boundary conditions based on nonlinear multidimensional characteristics

Cited by 20 publications

References 39 publications

Comparison of outflow boundary conditions for subsonic aeroacoustic simulations

Comparison of outflow boundary conditions for subsonic aeroacoustic simulations

Flow streamline based Navier–Stokes Characteristic Boundary Conditions: Modeling for transverse and corner outflows

Cross‐impact of beam local wavenumbers on the efficiency of self‐adaptive artificial boundary conditions for two‐dimensional nonlinear Schrödinger equation

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