Related papers: Refinement on non-hydrostatic shallow granular flo…
This paper introduces a novel mathematical framework for examining the regularity and energy dissipation properties of solutions to the stochastic Navier-Stokes equations. By integrating Sobolev-Besov hybrid spaces, fractional differential…
We parameterize sub-grid scale (SGS) fluxes in sinusoidally forced two-dimensional turbulence on the $\beta$-plane at high Reynolds numbers (Re$\sim$25000) using simple 2-layer Convolutional Neural Networks (CNN) having only…
Approximate deconvolution forms a mathematical framework for the structural modeling of turbulence. The sub-filter scale flow quantities are typically recovered by using the Van Cittert iterative procedure. In this paper, however, we put…
We study the problem of gravitational collapse in the context of scalar-tensor theories of Gravity. We introduce a new hydrodynamical formulation in the Einstein frame, inspired by that of Misner and Sharp. We obtain the equilibrium…
We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity…
We outline a program for obtaining an action principle for dissipative fluid dynamics by considering the holographic Wilsonian renormalization group applied to systems with a gravity dual. As a first step, in this paper we restrict to…
We propose IMEX HDG-DG schemes for planar and spherical shallow water systems. Of interest is subcritical flow, where the speed of the gravity wave is faster than that of nonlinear advection. In order to simulate these flows efficiently, we…
We design and compute first-order implicit-in-time variational schemes with high-order spatial discretization for initial value gradient flows in generalized optimal transport metric spaces. We first review some examples of gradient flows…
We perform a convergence analysis of a two-grid staggered solution algorithm for the Biot system modeling coupled flow and deformation in heterogeneous poroelastic media. The algorithm first solves the flow subproblem on a fine grid using a…
Flow transition from a stable to unstable states and eventually to turbulence is a classical fluid mechanics phenomenon with a strong practical relevance. Conventional hydrodynamic stability deals with perturbation dynamics on a steady…
This study discusses the necessity of anisotropic subgrid-scale (SGS) stress in large-eddy simulations (LESs) of turbulent shear flows using a coarse grid resolution. We decompose the SGS stress into two parts to observe the role of SGS…
The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear model reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with…
We present a method to simulate nonhydrostatic ocean flows on a horizontally-unstructured grid with a moving generalized vertical coordinate (GVC). The nonhydrostatic governing equations are transformed to a GVC system that can represent…
This work primarily focuses on the study of three gradient reconstruction techniques applied to the calculation of viscous terms in a cell-centered, finite volume formulation for general unstructured grids. The work also addresses different…
We present a further theoretical extension to the kinetic theory based formulation of the lattice Boltzmann method of Shan et al (2006). In addition to the higher order projection of the equilibrium distribution function and a sufficiently…
We describe an implicit general relativistic hydrodynamics code. The evolution equations are formulated in comoving coordinates. A conservative finite differencing of the Einstein equations is outlined, and artificial viscosity and…
In this paper, a new efficient and generalized consistency correction method for weakly-compressible smoothed particle hydrodynamics is proposed and successfully implemented in the simulation of violent free-surface flow exhibiting breaking…
In many engineering and industrial applications, the investigation of rotating turbulent flow is of great interest. In rotor-stator cavities, the centrifugal and Coriolis forces have a strong influence on the turbulence by producing a…
The high-order numerical solution of the non-linear shallow water equations (and of hyperbolic systems in general) is susceptible to unphysical Gibbs oscillations that form in the proximity of strong gradients. The solution to this problem…
This work focuses on the numerical computation of defocusing action ground states for rotating nonlinear Schr\"odinger equations (RNLS) using a direct gradient flow (DGF) method. We address theoretical gaps in the existing literature…