A moment model of shallow granular flows with variable friction laws
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918252241747968 |
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| author | Careaga, Julio Huang, Qian Koellermeier, Julian |
| author_facet | Careaga, Julio Huang, Qian Koellermeier, Julian |
| contents | In this work, we develop a modelling framework for granular flows based on the shallow water moment equations on inclined planes. Under the assumption of a polynomial expansion of the velocity field, the model extends the classical shallow water equations to vertically variable velocity profiles. The friction effects, which are captured through the strain-rate tensor, are incorporated into the model in two terms, the bulk and bottom friction. We propose a modelling procedure to incorporate general friction laws into our framework and exemplify this combining the Manning, Coulomb, Savage-Hutter, and $μ(I)$-rheology friction models in our modeling framework. Moreover, we develop a path-conservative finite volume numerical scheme based on the polynomial viscosity matrix method to properly handle the stiffness of the source terms. Numerical simulations are presented for different models of friction, including the case of wet-dry fronts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_15332 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A moment model of shallow granular flows with variable friction laws Careaga, Julio Huang, Qian Koellermeier, Julian Numerical Analysis Mathematical Physics 35L65, 76B15, 76M12 In this work, we develop a modelling framework for granular flows based on the shallow water moment equations on inclined planes. Under the assumption of a polynomial expansion of the velocity field, the model extends the classical shallow water equations to vertically variable velocity profiles. The friction effects, which are captured through the strain-rate tensor, are incorporated into the model in two terms, the bulk and bottom friction. We propose a modelling procedure to incorporate general friction laws into our framework and exemplify this combining the Manning, Coulomb, Savage-Hutter, and $μ(I)$-rheology friction models in our modeling framework. Moreover, we develop a path-conservative finite volume numerical scheme based on the polynomial viscosity matrix method to properly handle the stiffness of the source terms. Numerical simulations are presented for different models of friction, including the case of wet-dry fronts. |
| title | A moment model of shallow granular flows with variable friction laws |
| topic | Numerical Analysis Mathematical Physics 35L65, 76B15, 76M12 |
| url | https://arxiv.org/abs/2512.15332 |