Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
A unified hyperbolic formulation for viscous fluids and elastoplastic solids. / Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy.
Theory, Numerics and Applications of Hyperbolic Problems II. ed. / C Klingenberg; M Westdickenberg. Vol. 237 Springer New York LLC, 2018. p. 451-463 (Springer Proceedings in Mathematics & Statistics; Vol. 237).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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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 -
ID: 14405419