 Hyperbolic relaxation models for thin films down an inclined planeFiras Dhaouadi, Sergey Gavrilyuk and Jean-Paul Vila Applied Mathematics and Computation, 2022, vol. 433, issue C Abstract: We present a family of relaxation models for thin films flows where both viscosity and surface tension effects are inherent. In a first step, a first-order hyperbolic approximation to the dissipationless part of the system is presented. The method is based on an augmented Lagrangian approach, where a classical penalty method is used and high-order derivatives in the Lagrangian are promoted to new independent variables, for which hyperbolic closure equations are sought. Then, we show that the viscous terms can be treated either by plugging them directly to the obtained system, making it of the hyperbolic-parabolic type or by casting them into an approximate algebraic source term that is asymptotically equivalent to the former formulation. Finally, the extension of the method to a classical nonlinear surface tension model is also presented. Numerical results, for all the proposed models are shown and compared with experimental results and reference solutions. Keywords: Thin films; Fluid flows with surface tension; First-order hyperbolic equations; Finite volumes (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:433:y:2022:i:c:s0096300322004520 DOI: 10.1016/j.amc.2022.127378 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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