Imposing Boundary Conditions with the Injection, the Projection and the Simultaneous Approximation Term Methods

A simultaneous-approximation term is a non-reflecting boundary condition that is usually accompanied by summation-by-parts schemes for provable time stability. While a high-order convective flux based on reconstruction is often employed in a finite-volume method for compressible turbulent flow, finite-volume methods with the summation-by-parts property involve either equally weighted averaging or the second-order central flux for convective fluxes. In the present study, a cell-centered finite-volume method for compressible Naiver–Stokes equations was developed by combining a simultaneous-approximation term based on extrapolation and a low-dissipative discretization method without the summation-by-parts property. Direct numerical simulations and a large eddy simulation show that the resultant combination leads to comparable non-reflecting performance to that of the summation-by-parts scheme combined with the simultaneous-approximation term reported in the literature. Furthermore, a characteristic boundary condition was implemented for the present method, and its performance was compared with that of the simultaneous-approximation term for a direct numerical simulation and a large eddy simulation to show that the simultaneous-approximation term better maintained the average target pressure at the compressible flow outlet, which is useful for turbomachinery and aerodynamic applications, while the characteristic boundary condition better preserved the flow field near the outlet.

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A High Order Accurate Finite Difference Method for the Drinfel’d–Sokolov–Wilson Equation

Journal of Scientific Computing ◽

10.1007/s10915-021-01481-4 ◽

2021 ◽

Vol 88 (1) ◽

Author(s):

Ludvig Lindeberg ◽

Tuan Dao ◽

Ken Mattsson

Keyword(s):

Numerical Analysis ◽

Finite Difference Method ◽

Simultaneous Approximation ◽

Vries Equation ◽

Periodic Problem ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Wilson Equation ◽

Simultaneous Approximation Term ◽

Initial Boundary Value

AbstractWe analyse numerically the periodic problem and the initial boundary value problem of the Korteweg-de Vries equation and the Drindfeld–Sokolov–Wilson equation using the summation-by-parts simultaneous-approximation-term method. Two sets of boundary conditions are derived for each equation of which stability is shown using the energy method. Numerical analysis is done when the solution interacts with the boundaries. Results show the benefit of higher order SBP operators.

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Simultaneous-approximation-term based boundary discretization for moment equations of rarefied gas dynamics

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109243 ◽

2020 ◽

Vol 407 ◽

pp. 109243

Author(s):

Neeraj Sarna ◽

Harshit Kapadia ◽

Manuel Torrilhon

Keyword(s):

Gas Dynamics ◽

Simultaneous Approximation ◽

Rarefied Gas ◽

Rarefied Gas Dynamics ◽

Moment Equations ◽

Simultaneous Approximation Term

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Accuracy of the Simultaneous-Approximation-Term Boundary Condition for Time-Dependent Problems

Journal of Scientific Computing ◽

10.1007/s10915-010-9347-4 ◽

2010 ◽

Vol 43 (1) ◽

pp. 118-133 ◽

Cited By ~ 54

Author(s):

Daniel J. Bodony

Keyword(s):

Boundary Condition ◽

Simultaneous Approximation ◽

Time Dependent ◽

Simultaneous Approximation Term ◽

Time Dependent Problems

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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