Mathematical study on the thickened interface model by viscosity solution of the level-set equation

Abstract

The level-set approach extended for its viscosity solution is investigated to derive a relation to the conservation law of fluid phenomena and the phase-field approach based on the free energy theory. This mathematical approach is useful to consider approximate models for fluid interface problems. Here, this approach is applied to the thickened interface model of the combustion flame problem to derive a new mathematical formulation by the viscosity solution of the level-set equation, which can maintain a flame propagation speed of global solution. This approach reveals a mathematical incompatibility of empirical thickened flame models and proposes some improvements.

Keywords

• level-set equation
• viscosity solution
• combustion flame
• thickened interface model
• conservation law
• phase field approach