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Resolvent analysis of the linearized Navier-Stokes equations provides useful insight into the dynamics of transitional and turbulent flows and can provide a model for the dominant coherent structures within the flow, particularly for flows…
Direct methods to obtain global stability modes are restricted by the daunting sizes and complexity of Jacobians encountered in general three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi methods have greatly…
For more than 150 years the Navier-Stokes equations for thermodynamically quasi-equilibrium flows have been the cornerstone of modern computational fluid dynamics that underpins new fluid technologies. However, the applicable regime of the…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/artificial disturbances could be neglected. Is this assumption…
In this paper, we describe a numerical algorithm for the self-consistent simulations of surface water and sediment dynamics. The method is based on the original Lagrangian-Eulerian CSPH-TVD approach for solving the Saint-Venant and Exner…
Computational fluid dynamics (CFD) solvers employing two-equation eddy viscosity models are the industry standard for simulating turbulent flows using the Reynolds-averaged Navier-Stokes (RANS) formulation. While these methods are…
We propose to accelerate a high order discontinuous Galerkin solver using neural networks. We include a corrective forcing to a low polynomial order simulation to enhance its accuracy. The forcing is obtained by training a deep fully…
This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…
Computational fluid dynamics (CFD) can be used to simulate vascular haemodynamics and analyse potential treatment options. CFD has shown to be beneficial in improving patient outcomes. However, the implementation of CFD for routine clinical…
The viscosity of supercooled liquids notably increases with decreasing temperature, leading to solidification through a glass transition. This process is accompanied by dynamic heterogeneity, characterized by persistent dynamic spatial…
In this paper the issue of the determination of the fluid pressure in incompressible fluids is addressed, with particular reference to the search of algorithms which permit to advance in time the fluid pressure without actually solving…
We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…
We introduce a coupled Cahn-Hilliard Navier-Stokes model that governs the two-phase dynamics of a system that consists of a fluid and a solid phase and prove its thermodynamic consistency. Moreover, we present an associated fully-discrete…
Nowadays, Computational Fluid Dynamics (CFD) is a fundamental tool for industrial design. However, the computational cost of doing such simulations is expensive and can be detrimental for real-world use cases where many simulations are…
Simulating complex dynamics like fluids with traditional simulators is computationally challenging. Deep learning models have been proposed as an efficient alternative, extending or replacing parts of traditional simulators. We investigate…
The accuracy and stability of implicit CFD codes are frequently impaired by the decoupling between variables, which can ultimately lead to numerical divergence. Coupled solvers, which solve all the governing equations simultaneously, have…
The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in $\mathbb{R}^3$. For the resulting Navier-Stokes type system, posed on a smooth closed…
To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale framework was proposed in this paper by applying a physics-guided data-driven approach. Instrumental to this framework, Feature Similarity…
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…