A new model of first order hyperbolic continuum mechanics solved with high order ADER schemes

Dr Olindo Zanotti (University of Trento)

Thursday 6th October, 2022 14:00-15:00 Maths 311B / ZOOM (ID: 894 4545 5110)

Abstract

I will describe a new, unified first order hyperbolic formulation of continuum mechanics that includes at the same time inviscid and viscous heat conducting fluids, as well as elastic and visco-plastic solids. The two key elements of the mathematical formulation are i) the formulation of all constitutive relations as partial derivatives of an energy potential E and ii) the temporal evolution of a distortion tensor A, from which the viscous stresses of the fluid can be directly obtained, like the shear stresses in solid mechanics. Actually, viscous fluids are treated by the underlying nonlinear hyper-elastic model as generalized visco-plastic solids. This is achieved via a stiff relaxation source term that accounts for strain relaxation in the evolution equations of A. The extension to magnetohydrodynamics is also considered briefly. In addition, I will show the numerical validation of the model through a large set of test problems solved by means of high order ADERWENO finite volume and ADER discontinuous Galerkin schemes, comparing with exact or numerical reference solutions of the Navier-Stokes equations (for viscous fluids) and comparing also with the equations of linear elasticity (for elastic solids).

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