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Energy-conserving scheme for a shallow-water model with capillary effects
arXiv cs.NA0 views
arXiv:2611.07360v1 Announce Type: new Abstract: We consider numerical approximations of shallow-water and thin-film flow models with capillary effects. These models lead to third-order differential equations, and we work with an augmented model with second-order derivatives. For a wide class of such models, which includes the classical shallow-water model and thin-film flow models, we develop a fully discrete energy-conserving scheme for both the quadratic and fully nonlinear capillary models. Numerical results show that the proposed scheme is stable and conserves total energy in the absence of dissipative effects.
Source：https://arxiv.org/abs/2611.07360PreviousA physics-based adaptive low-rank method for 6D Vlasov simulationsNextAsymptotic-Preserving Tensor Neural Networks for 3D High-Field Kinetic Equations with Applications to Uncertainty Quantification
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