Related papers: Primitive variable regularization to derive novel …
In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and…
We show existence of global strong solutions with large initial data on the irrotational part for the shallow-water system in dimension $N\geq 2$. We introduce a new notion of \textit{quasi-solutions} when the initial velocity is assumed to…
In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced for the surrogate modeling of high-fidelity turbulent flow…
Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods…
Computational fluid dynamics models based on Reynolds-averaged Navier--Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
Normalizing flows are a powerful class of generative models demonstrating strong performance in several speech and vision problems. In contrast to other generative models, normalizing flows are latent variable models with tractable…
Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
We use dynamical systems theory to construct the normal form of the Navier--Stokes equations for the flow of a thin layer of fluid upon a solid substrate. The normal form equations illuminate the fluid dynamics by decoupling the long-term…
We present and discuss a novel approach to deal with conservation properties for the simulation of nonlinear complex porous media flows in the presence of: 1) multiscale heterogeneity structures appearing in the elliptic-pressure-velocity…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
In this work, we propose a second-order accurate scheme for shallow water equations in general covariant coordinates over manifolds. In particular, the covariant parametrization in general covariant coordinates is induced by the metric…
We investigate a two-parameter hyperbolic relaxation approximation to the incompressible Navier-Stokes equations, incorporating a first-order relaxation and the artificial compressibility method. With vanishingly small perturbations of…
The fourth-gradient model for fluids-associated with an extended molecular mean-field theory of capillarity-is considered. By producing fluctuations of density near the critical point like in computational molecular dynamics, the model is…
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…
By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the…
The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to implement with high-order numerical methods. The regularized…
Extending results of Oh--Zumbrun and Johnson--Zumbrun for parabolic conservation laws, we show that spectral stability implies nonlinear stability for spatially periodic viscous roll wave solutions of the one-dimensional St. Venant…