15 research outputs found
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A diffuse interface model for quasi-incrompressible flows : sharp interface limits and numerics
In this contribution, we investigate a diffuse interface model for quasi–incompressible flows. We determine corresponding sharp interface limits of two different scalings. The sharp interface limit is deduced by matched asymptotic expansions of the fields in powers of the interface. In particular, we study solutions of the derived system of inner equations and discuss the results within the general setting of jump conditions for sharp interface models. Furthermore, we treat, as a subproblem, the convective Cahn–Hilliard equation numerically by a Local Discontinuous Galerkin scheme
A diffuse interface model for quasi-incompressible flows: Sharp interface limits and numerics
In this contribution, we investigate a diffuse interface model for quasi-incompressible flows. We determine corresponding sharp interface limits of two different scalings. The sharp interface limit is deduced by matched asymptotic expansions of the fields in powers of the interface. In particular, we study solutions of the derived system of inner equations and discuss the results within the general setting of jump conditions for sharp interface models. Furthermore, we treat, as a subproblem, the convective Cahn-Hilliard equation numerically by a Local Discontinuous Galerkin scheme
Pressure reconstruction for weak solutions of the two-phase incompressible Navier–Stokes equations with surface tension
For the two-phase incompressible Navier–Stokes equations with surface tension, we derive an appropriate weak formulation incorporating a variational formulation using divergence-free test functions. We prove a consistency result to justify our definition and, under reasonable regularity assumptions, we reconstruct the pressure function from the weak formulation
Recommended from our members
Pressure reconstruction for weak solutions of the two-phase incompressible Navier--Stokes equations with surface tension
For the two-phase incompressible Navier--Stokes equations with surface tension, we derive an appropriate weak formulation incorporating a variational formulation using divergence-free test functions. We prove a consistency result to justify our definition and, under reasonable regularity assumptions, we reconstruct the pressure function from the weak formulation
A diffuse interface model for quasi–incompressible flows : Sharp interface limits and numerics
In this contribution, we investigate a diffuse interface model for quasi–incompressible
flows. We determine corresponding sharp interface limits of two different scalings. The
sharp interface limit is deduced by matched asymptotic expansions of the fields in powers
of the interface. In particular, we study solutions of the derived system of inner
equations and discuss the results within the general setting of jump conditions for sharp
interface models. Furthermore, we treat, as a subproblem, the convective Cahn–Hilliard
equation numerically by a Local Discontinuous Galerkin scheme