Volume 13, Issue 2
A Finite Volume Scheme for Savage-Hutter Equations on Unstructured Grids

Ruo Li & Xiaohua Zhang

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 479-496.

Published online: 2020-03

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  • Abstract

A Godunov-type finite volume scheme on unstructured grids is proposed to numerically solve the Savage-Hutter equations in curvilinear coordinate. We show the direct observation that the model isn't a Galilean invariant system. At the cell boundary, the modified Harten-Lax-van Leer (HLL) approximate Riemann solver is adopted to calculate the numerical flux. The modified HLL flux is not troubled by the lack of Galilean invariance of the model and it is helpful to handle discontinuities at free interface. Rigidly the system is not always a hyperbolic system due to the dependence of flux on the velocity gradient. Even so, our numerical results still show quite good agreements with reference solutions. The simulations for granular avalanche flows with shock waves indicate that the scheme is applicable.

  • Keywords

Granular avalanche flow, Savage-Hutter equations, finite volume method, Galilean invariant.

  • AMS Subject Headings

65M10, 65M15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

rli@math.pku.edu.cn (Ruo Li)

zhangxiaohua07@163.com (Xiaohua Zhang)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-13-479, author = {Li , Ruo and Zhang , Xiaohua}, title = {A Finite Volume Scheme for Savage-Hutter Equations on Unstructured Grids}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {2}, pages = {479--496}, abstract = {

A Godunov-type finite volume scheme on unstructured grids is proposed to numerically solve the Savage-Hutter equations in curvilinear coordinate. We show the direct observation that the model isn't a Galilean invariant system. At the cell boundary, the modified Harten-Lax-van Leer (HLL) approximate Riemann solver is adopted to calculate the numerical flux. The modified HLL flux is not troubled by the lack of Galilean invariance of the model and it is helpful to handle discontinuities at free interface. Rigidly the system is not always a hyperbolic system due to the dependence of flux on the velocity gradient. Even so, our numerical results still show quite good agreements with reference solutions. The simulations for granular avalanche flows with shock waves indicate that the scheme is applicable.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0080}, url = {http://global-sci.org/intro/article_detail/nmtma/15488.html} }
TY - JOUR T1 - A Finite Volume Scheme for Savage-Hutter Equations on Unstructured Grids AU - Li , Ruo AU - Zhang , Xiaohua JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 479 EP - 496 PY - 2020 DA - 2020/03 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0080 UR - https://global-sci.org/intro/article_detail/nmtma/15488.html KW - Granular avalanche flow, Savage-Hutter equations, finite volume method, Galilean invariant. AB -

A Godunov-type finite volume scheme on unstructured grids is proposed to numerically solve the Savage-Hutter equations in curvilinear coordinate. We show the direct observation that the model isn't a Galilean invariant system. At the cell boundary, the modified Harten-Lax-van Leer (HLL) approximate Riemann solver is adopted to calculate the numerical flux. The modified HLL flux is not troubled by the lack of Galilean invariance of the model and it is helpful to handle discontinuities at free interface. Rigidly the system is not always a hyperbolic system due to the dependence of flux on the velocity gradient. Even so, our numerical results still show quite good agreements with reference solutions. The simulations for granular avalanche flows with shock waves indicate that the scheme is applicable.

Ruo Li & Xiaohua Zhang. (2020). A Finite Volume Scheme for Savage-Hutter Equations on Unstructured Grids. Numerical Mathematics: Theory, Methods and Applications. 13 (2). 479-496. doi:10.4208/nmtma.OA-2019-0080
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