Compressible, multiphase semi-implicit method with moment of fluid interface representation

Abstract

A unified method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated SemiLagrangian advection algorithm is presented. The deforming material boundaries are represented using the moment-of-fluid method. The new algorithm uses a semi-implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed. The asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows including stiff materials; enabling large time

Incompressible multiphase flow and encapsulation simulations using the moment‐of‐fluid method

“…where I is a momentum preserving interpolation operator (Kwatra et al, 2009;Jemison et al, 2014) and the discretized surface tension forces, F tension and F M AC,tension , are defined above by equations (32) and (33).…”

“…Interpolate the pressure p found in (43) from cell centers to face centers using the condition of constant contact (Kwatra et al, 2009;Jemison et al, 2014) and then update the new cell centered velocity:…”

“…It is required to interpolate the cell centered pressure to the cell faces. As in (Kwatra et al, 2009;Jemison et al, 2014), we define the momentum equation in each half cell region, Ω i,R and Ω i+1,L :…”

“…Recently, the moment of fluid (MOF) method (Dyadechko and Shashkov, 2005;Ahn and Shashkov, 2007;Dyadechko and Shashkov, 2008;Jemison et al, 2013Jemison et al, , 2014Jemison et al, , 2015 has been developed. In addition to the volume fraction function used in the VOF method, the MOF method considers the material centroid information in the interface reconstruction process and can be considered a generalization of the VOF method.…”

“…As in (Jemison et al, 2014), we maintain and update the velocity at both cell centers and face centers. The velocity is interpolated from cell centers to face centers using mass weighting where the MOF reconstruction determines the weights.…”