An exactly curl-free staggered semi-implicit finite volume scheme for a first order hyperbolic model of viscous flow with surface tension

by   Simone Chiocchetti, et al.

In this paper, we present a semi-implicit numerical solver for a first order hyperbolic formulation of two-phase flow with surface tension and viscosity. The numerical method addresses several complexities presented by the PDE system in consideration: (i) The presence of involution constraints of curl type in the governing equations requires explicit enforcement of the zero-curl property of certain vector fields (an interface field and a distortion field); the problem is eliminated entirely by adopting a set of compatible curl and gradient discrete differential operators on a staggered grid, allowing to preserve the Schwartz identity of cross-derivatives exactly. (ii) The evolution equations feature highly nonlinear stiff algebraic source terms which are used for the description of viscous interactions as emergent behaviour of an elasto-plastic solid in the stiff strain relaxation limit; such source terms are reliably integrated with an efficient semi-analytical technique. (iii) In the low-Mach number regime, standard explicit Godunov-type schemes lose efficiency and accuracy; the issue is addressed by means of a simple semi-implicit, pressure-based, split treatment of acoustic and non-acoustic waves, again using staggered grids that recover the implicit solution for a single scalar field (the pressure) through a sequence of symmetric-positive definite linear systems that can be efficiently solved via the conjugate gradient method.


page 1

page 2

page 3

page 4


A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics

We propose a new pressure-based structure-preserving (SP) and quasi asym...

A novel structure preserving semi-implicit finite volume method for viscous and resistive magnetohydrodynamics

In this work we introduce a novel semi-implicit structure-preserving fin...

An all Mach number finite volume method for isentropic two-phase flow

We present an implicit-explicit finite volume scheme for isentropic two ...

A new instability in clustering dark energy?

In this paper, we study the effective field theory (EFT) of dark energy ...

Please sign up or login with your details

Forgot password? Click here to reset