Sur une méthode de pénalisation tensorielle pour la résolution des équations de Navier–Stokes

Abstract

An original reformulation of the viscous stress tensor is proposed for the motion equations dedicated to an incompressible fluid. Four different tensors appear in this decomposition, associated with viscosities of compression, elongation, shearing and rotation. This new model allows us to build a numerical solver of the Navier–Stokes equations based on a technique of tensorial penalization which is generalized with all the stresses acting on a flow. The processing of incompressibility and the rotation of a rigid body in a flow are described thanks to the model. Several numerical applications are proposed to illustrate the abilities of the new penalization method.