Related papers: Primitive variable regularization to derive novel …
We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by…
A multi-scale method for the hyperbolic systems governing sediment transport in subcritical case is developed. The scale separation of this problem is due to the fact that the sediment transport is much slower than flow velocity. We first…
We present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the original entropy-based moment method, and this gives the…
A new slender-body theory for viscous flow, based on the concepts of dimensional reduction and hyperviscous regularization, is presented. The geometry of flat, elongated, or point-like rigid bodies immersed in a viscous fluid is…
Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
The purpose of this paper is to derive rigorously the so called viscous shallow water equations given for instance page 958-959 in [A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys, 69 (1997), 931?980]. Such a system of equations is…
We propose a variational framework for the resolution of a non-hydrostatic Saint-Venant type model with bottom topography. This model is a shallow water type approximation of the incompressible Euler system with free surface and slightly…
Numerous codes are being developed to solve Shallow Water equations. Because there are used in hydraulic and environmental studies, their capability to simulate properly flow dynamics is critical to guarantee infrastructure and human…
The stability of Lattice Boltzmann Equations modelling Shallow Water Equations in the special case of reduced gravity is investigated theoretically. A stability notion is defined as applied in incompressible Navier-Stokes equations in…
Numerical simulations are a valuable research and layout tool for fluid flow problems, yet repeated evaluations of parametrized problems, necessary to solve optimization problems, can be very costly. One option to speed up this process is…
In this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems…
We make a brief historical review to the moment model reduction to the kinetic equations, particularly the Grad's moment method for Boltzmann equation. The focus is on the hyperbolicity of the reduced model, which is essential to the…
The relativistic method of moments is one of the most successful approaches to extract second order viscous hydrodynamics from a kinetic underlying background. The equations can be systematically improved to higher order, and they have…
A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…
This paper is dedicated to the study of both viscous compressible barotropic fluids and Navier-Stokes equation with dependent density, when the viscosity coefficients are variable, in dimension $d\geq2$. We aim at proving the local and…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…
We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discretization using shifted base functions. Model-order…