In this paper, complete Riemann solver of Osher-Solomon and the HLLEM Riemann solver for unified first order hyperbolic formulation of continuum mechanics, which describes both of fluid and solid dynamics, are presented. This is the first time that these types of Riemann solvers are applied to such a complex system of governing equations as the GPR model of continuum mechanics. The first order hyperbolic formulation of continuum mechanics recently proposed by Godunov S. K., Peshkov I. M. and Romenski E. I., further denoted as GPR model includes a hyperbolic formulation of heat conduction and an overdetermined system of PDE. Path-conservative schemes are essential in order to give a sense to the non-conservative terms in the weak solution framework since governing PDE system contains non-conservative products, too. New Riemann solvers are implemented and tested successfully, which means it certainly acts better than standard local Lax-Friedrichs-type or Rusanov-type Riemann solvers. Two simple computational examples are presented, but the obtained computational results clearly show that the complete Riemann solvers are less dissipative than the simple Rusanov method that was employed in previous work on the GPR model.

Ariunaa Uuriintsetseg, MSc, Senior Lecturer, Mongolian University of Science and Technology, 34, Baga toiruu, Sukhbaatar district, Ulaanbaatar, 14191, Mongolia, tel.: +976 997-373-68, email: ariunaa@must.edu.mn

Michael Dumbser, Dr. Sci. (Tech.), Full Professor, University of Trento, 77, Via Mesiano, Trento, 38050, Italy, tel.:+39-461 882-646, email: michael.dumbser@unitn.it

Sarantuya Tsedendamba, Dr. Sci. (Phys.– Math.), Prof., Mongolian University of Science and Technology, 34, Baga toiruu, Sukhbaatar district, Ulaanbaatar, 14191, Mongolia, tel.: +976 991-280-63, email: saraa@must.edu.mn

Ariunaa U., Dumbser M., Sarantuya Ts. Complete Riemann Solvers for the Hyperbolic GPR Model of Continuum Mechanics. The Bulletin of Irkutsk State University. Series Mathematics, 2021, vol. 35, pp. 60-72. https://doi.org/10.26516/1997-7670.2021.35.60

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