A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios

An Eulerian method to numerically solve incompressible bifluid problems with high density ratio is presented. This method can be considered as an improvement of the Ghost Fluid method, with the specificity of a sharp second-order numerical scheme for the spatial resolution of the discontinuous elliptic problem for the pressure. The Navier–Stokes equations are integrated in time with a fractional step method based on the Chorin scheme and discretized in space on a Cartesian mesh. The bifluid interface is implicitly represented using a level-set function. The advantage of this method is its simplicity to implement in a standard monofluid Navier–Stokes solver while being more accurate and conservative than other simple classical bifluid methods. The numerical tests highlight the improvements obtained with this sharp method compared to the reference standard first-order methods.

Download Full-text

A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-06-2015-0233 ◽

2016 ◽

Vol 26 (3/4) ◽

pp. 595-623 ◽

Cited By ~ 14

Author(s):

Rhodri LT Bevan ◽

Etienne Boileau ◽

Raoul van Loon ◽

R.W. Lewis ◽

P Nithiarasu

Keyword(s):

Incompressible Flows ◽

Transient Flow ◽

Stokes Equations ◽

Second Order ◽

Fractional Step ◽

Step Method ◽

Fractional Step Method ◽

Content Type ◽

Time Stepping ◽

Implicit Form

Purpose – The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not to reproduce the extensive contributions on the subject, but to report on long-term experience with and provide a unified overview of a particular approach: the characteristic-based split method. Three procedures, the semi-implicit, quasi-implicit and fully explicit, are studied and compared. Design/methodology/approach – This work provides a thorough assessment of the accuracy and efficiency of these schemes, both for a first and second order pressure split. Findings – In transient problems, the quasi-implicit form significantly outperforms the fully explicit approach. The second order (pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully explicit method, utilising artificial compressibility and a pseudo time stepping procedure, requires no second order fractional split to achieve second order or higher accuracy. While the fully explicit form is efficient for steady state problems, due to its ability to handle local time stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations. Originality/value – A comprehensive comparison between three versions of the CBS method is provided for the first time.

Download Full-text

NUMERICAL SIMULATION OF ISOTHERMAL AND THERMAL TWO-PHASE FLOWS USING PHASE-FIELD MODELING

International Journal of Modern Physics C ◽

10.1142/s0129183107010772 ◽

2007 ◽

Vol 18 (04) ◽

pp. 536-545 ◽

Cited By ~ 5

Author(s):

NAOKI TAKADA ◽

AKIO TOMIYAMA

Keyword(s):

Phase Field ◽

Stokes Equations ◽

Density Ratio ◽

Navier Stokes ◽

Phase Field Modeling ◽

Two Phase Flows ◽

Two Phase ◽

Navier Stokes Equations ◽

Field Modeling ◽

High Density Ratio

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, we examined the applicability of two versions of computational fluid dynamics method, NS-PFM, combining Navier-Stokes equations with phase-field modeling for interface based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

Download Full-text