A new model for shallow elastic fluids

Details A new model for shallow elastic fluids A new model for shallow elastic fluids

2011-10-04

arxiv.org/abs/1110.0799v1

Mathematics

Numerical Analysis

Part of this work was completed while Sebastien Boyaval was an academic host at MATHICSE- ASN chair (EPFL). SB would like to t

Scientific paper

We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order epsilon, the aspect ratio of the thin layer of fluid), but the relaxation time is kept finite. Additionally to the classical layer depth and velocity in shallow models, our system describes also the evolution of two scalar stresses. It has an intrinsic energy equation. The mathematical properties of the model are established, an important feature being the non-convexity of the physically relevant energy with respect to conservative variables, but the convexity with respect to the physically relevant pseudo-conservative variables. Numerical illustrations are given, based on a suitable well-balanced finite-volume discretization involving an approximate Riemann solver.

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