A diagonally dominant second-order accurate implicit scheme

Khosla, P. K.; Rubin, S. G.

doi:10.1016/0045-7930(74)90014-0

Cited by 432 publications

(174 citation statements)

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“…35 We have chosen the second-order SMART scheme. 16,17 From our experience, it perfectly fits the requirements needed for an accurate charge density solution.…”

Section: B Charge Density Equation Treatmentmentioning

confidence: 99%

Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection

2012

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Two-dimensional numerical simulations are carried out to examine the problem of transient electroconvection stability of dielectric liquids subjected to unipolar injection. The entire set of electrohydrodynamics equations associated with the electroconvective phenomena that occur in a layer of a dielectric liquid between two parallel electrodes subjected to a potential difference are solved numerically. We first validate the numerical simulation by comparing our linear stability electroconvection criteria with those obtained by other authors with a stability approach. In this paper, we restrict the study to the strong injection case, which corresponds to values of the non-dimensional injection parameter C greater than or equal to 10. The numerical solution of the electroconvective problem is then presented for rigid lateral boundary conditions. A detailed analysis of the scenario that occurs for different characteristic values of the stability parameter T is provided. The flow structure and its behaviour highlight the existence of different regimes, from laminar to chaotic. The development of charged plumes has been observed in particular. We compute the electrical Nusselt number for different values of the stability parameter and ion mobility. The electrical Nusselt number saturates with increasing T, a fact that it is in agreement with available experimental data. Finally, a spectral analysis is conducted for different aspect ratios of the computational domain. The spectral analysis gives an insight into the physical origin of the velocity and current oscillations. C 2012 American Institute of Physics. [http://dx

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“…35 We have chosen the second-order SMART scheme. 16,17 From our experience, it perfectly fits the requirements needed for an accurate charge density solution.…”

Section: B Charge Density Equation Treatmentmentioning

confidence: 99%

Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection

2012

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“…The pressure/velocity coupling is ensured using the SIMPLE algorithm. The convective terms are discretized utilising the third order Quadratic Upstream Interpolation for Convective Kinematics (QUICK), Khosla et al [21]. …”

Section: Computational Configurationmentioning

confidence: 99%

Self-Similarity and helical symmetry in vortex generator flow simulations

Fernández

Velte

Réthore

et al. 2014

J. Phys.: Conf. Ser.

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Abstract. According to experimental observations, the vortices generated by vortex generators have previously been observed to be self-similar for both the axial (u z ) and azimuthal (u Ө ) velocity profiles. Further, the measured vortices have been observed to obey the criteria for helical symmetry. This is a powerful result, since it reduces the highly complex flow to merely four parameters. In the present work, corresponding computer simulations using ReynoldsAveraged Navier-Stokes equations have been carried out and compared to the experimental observations. The main objective of this study is to investigate how well the simulations can reproduce the physics of the flow and if the same analytical model can be applied. Using this model, parametric studies can be significantly reduced and, further, reliable simulations can substantially reduce the costs of the parametric studies themselves.

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“…A simple, but effective way to achieve these objectives is to use the deferred correction strategy (e.g. [7,8]). A high-order approximate expression for computing the convected face value is cast as the upstream value (the first-order upwinding scheme) and the streamwise correction term which are then treated implicitly and explicitly, respectively.…”

Section: Introductionmentioning

confidence: 99%

A high‐order upwind control‐volume method based on integrated RBFs for fluid‐flow problems

Mai‐Duy

Tran-Cong

2010

Numerical Methods in Fluids

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1Summary This paper is concerned with the development of a high-order upwind conservative discretisation method for the simulation of flows of a Newtonian fluid in two dimensions. The fluid-flow domain is discretised using a Cartesian grid from which nonoverlapping rectangular control-volumes are formed. Line integrals arising from the integration of the diffusion and convection terms over control volumes are evaluated using the middle-point rule. One-dimensional integrated radial basis function schemes using the multiquadric basis function are employed to represent the variations of the field variables along the grid lines. The convection term is effectively treated using an upwind scheme with the deferred-correction strategy. Several highly-nonlinear test problems governed by the Burgers and the Navier-Stokes equations are simulated, which show that the proposed technique is stable, accurate and converges well.

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A diagonally dominant second-order accurate implicit scheme

Cited by 432 publications

References 1 publication

Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection

Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection

Self-Similarity and helical symmetry in vortex generator flow simulations

A high‐order upwind control‐volume method based on integrated RBFs for fluid‐flow problems

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