TY - GEN

T1 - A unified hyperbolic formulation for viscous fluids and elastoplastic solids

AU - Dumbser, Michael

AU - Peshkov, Ilya

AU - Romenski, Evgeniy

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics and solid dynamics. The fundamental difference from the classical continuum models, such as the Navier–Stokes, for example, is that the finite length scale of the continuum particles is not ignored but kept in the model in order to semi-explicitly describe the essence of any flows, that is the process of continuum particles rearrangements. To allow the continuum particle rearrangements, we admit the deformability of particle which is described by the distortion field. The ability of media to flow is characterized by the strain dissipation time which is a characteristic time necessary for a continuum particle to rearrange with one of its neighboring particles. It is shown that the continuum particle length scale is intimately connected with the dissipation time. The governing equations are represented by a system of first-order hyperbolic PDEs with source terms modeling the dissipation due to particle rearrangements. Numerical examples justifying the reliability of the proposed approach are demonstrated.

AB - We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics and solid dynamics. The fundamental difference from the classical continuum models, such as the Navier–Stokes, for example, is that the finite length scale of the continuum particles is not ignored but kept in the model in order to semi-explicitly describe the essence of any flows, that is the process of continuum particles rearrangements. To allow the continuum particle rearrangements, we admit the deformability of particle which is described by the distortion field. The ability of media to flow is characterized by the strain dissipation time which is a characteristic time necessary for a continuum particle to rearrange with one of its neighboring particles. It is shown that the continuum particle length scale is intimately connected with the dissipation time. The governing equations are represented by a system of first-order hyperbolic PDEs with source terms modeling the dissipation due to particle rearrangements. Numerical examples justifying the reliability of the proposed approach are demonstrated.

KW - Hyperbolic equations

KW - Unified flow theory

KW - Viscous fluids Elastoplasticity

KW - Elastoplasticity

KW - SOUND

KW - Viscous fluids

KW - HIGH-VELOCITY IMPACT

KW - NONLINEAR MODEL

KW - SCHEMES

UR - http://www.scopus.com/inward/record.url?scp=85049444041&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-91548-7_34

DO - 10.1007/978-3-319-91548-7_34

M3 - Conference contribution

AN - SCOPUS:85049444041

SN - 9783319915470

VL - 237

T3 - Springer Proceedings in Mathematics & Statistics

SP - 451

EP - 463

BT - Theory, Numerics and Applications of Hyperbolic Problems II

A2 - Klingenberg, C

A2 - Westdickenberg, M

PB - Springer New York LLC

T2 - 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016

Y2 - 1 August 2016 through 5 August 2016

ER -