Elastic capsule deformation in general irrotational linear flows

Irrotational flows for Chaplygin gas. Conical waves

Remark that real flows should be non-isentropic. The constancy of the entropy is not compatible once shock waves develop. It is only expected that the amplitude of oscillations for the entropy are of cubic order with respect to those of the flow. There is one notable exception, that of a Chaplygin gas, whose pressure has the form p(ρ, s) = g(s)− f(s)/ρ ; then the entropy remains constant even b...

Numerical simulation of non-linear elastic flows with a general collocated finite-volume method

This paper reports the development and application of a finite-volume based methodology for the calculation of the flow of fluids which follow differential viscoelastic constitutive models. The novelty of the method lies on the use of the non-staggered grid arrangement, in which all dependent variables are located at the center of the control volumes, thus greatly simplifying the adoption of ge...

Three-dimensional Interaction of Shocks in Irrotational Flows

The general d-dimensional Riemann problem raises naturally the question of resolving the interaction of d planar shocks merging at a point. In gas dynamics, we may consider only standing shocks. This problem has received a satisfactory answer in dimension d = 2 (see [2, 3]). We investigate the 3-dimensional case. We restrict to the irrotational case, in order to keep the complexity of the solut...

Control of Underwater Vehicles in Inviscid Fluids. I: Irrotational Flows

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with t...

Elastic Fibers in Flows