Artificial compressibility, characteristics-based schemes for variable-density, incompressible, multispecies flows: Part II. Multigrid implementation and numerical tests

Abstract

The paper presents an investigation of the accuracy and efficiency of artificial compressibility, characteristics-based (CB) schemes for variable-density incompressible flows. The CB schemes have been implemented in conjunction with a multigrid method for accelerating numerical convergence and a fourth-order, explicit Runge-Kutta method for the integration of the governing equations in time. The implementation of the CB schemes is obtained in conjunction with first-, second-and third-order interpolation formulas for calculating the variables at the cell faces of the computational volume. The accuracy and efficiency of the schemes are examined against analytical and experimental results for diffusion broadening in two-and three-dimensional microfluidic channels, a problem that has motivated the development of the present methods. Moreover, unsteady, inviscid simulations have been performed for variable-density mixing layer. The computations revealed that accuracy and efficiency depend on the CB scheme design. The best multigrid convergence rates were exhibited by the conservative CB scheme, which is obtained by the fully conservative formulation of the variable-density, incompressible equations.

Interface Capturing in Dual-Flow Microfluidics

“…Doubling the grid size in each direction of the cross-section altered the velocity magnitude at the interface by 1.3%. Validation of the CFD models used in this paper was reported previously by Shapiro and Drikakis 11,12 for HR-CBS and by Shapiro et al 8 for PC-VOF.…”

“…The above system is solved using a high-resolution characteristic-based scheme (hereafter referred to as HR-CBS) developed for multi-component flows by Shapiro and Drikakis 11,12 . The pressure-correction-based computations were performed using first and secondorder accurate upwind schemes in conjunction with the SIMPLE pressure-velocity coupling and Volume of Fluid interface tracking method (hereafter referred to as PC-VOF) 13 as provided by the commercial code FLUENT (Fluent 6.2.16); the additional volumefraction equation was for xylene.…”

“…The aim of this paper is to present a comparative study of two different computational fluid dynamics methods for modelling the interface position: (i) a high-resolution characteristics-based scheme 11,12 and (ii) a traditional pressure-correction based algorithms applied in conjunction with Volume Of Fluid (VOF) interface tracking 13 . For a two-dimensional flow setup, an analytic solution for the position of the interface is derived and used to assess the accuracy of the above schemes in the developed flow region.…”

On stability condition for bifluid flows with surface tension: Application to microfluidics

“…In a series of papers, Yu, Sakai and Sethian [56][57][58] perform abundant numerical simulations of ink-jet printing for both Newtonian and viscoelastic fluids ; in these applications, the Reynolds number is rather high, namely 40 to 90. Shapiro and Drikakis [40] developed specific methods for diffusion broadening in two-and three-dimensional microfluidic channels. De Menech performed simulation of droplet breakup in a microfluidic junction, with a phase field method [27].…”

Genuinely multidimensional characteristic‐based scheme for incompressible flows

“…Siong et al used a CB implicit finite-volume method for calculating incompressible flow in porous media on unstructured grids [16]. Drikakis and Shapiro applied the artificial compressibility method for solving flows with various densities by using a locally one-dimensional characteristic scheme [17,18]. Other case studies about using the CB schemes in conjunction with artificial compressibility for modeling incompressible flow can be found in References [19][20][21][22][23].…”