相关论文: A massively parallel Eulerian-Lagrangian method fo…

Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…

We propose two closely--related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and…

The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial…

The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too…

The explicit semi-Lagrangian method method for solution of Lagrangian transport equations as developed in [Natarajan and Jacobs, Computer and Fluids, 2020] is adopted for the solution of stochastic differential equations that is consistent…

Our work is motivated by the analysis of ash plume dynamics, arising in the study of volcanic eruptions. Such phenomena are characterized by large Reynolds number (exceeding $10^7$) and a large number of polydispersed particles~[1]. Thus,…

We propose a new Eulerian-Lagrangian (EL) discontinuous Galerkin (DG) method. The method is designed as a generalization of the semi-Lagrangian (SL) DG method for linear advection problems proposed in [J. Sci. Comput. 73: 514-542, 2017],…

We propose a new Eulerian-Lagrangian Runge-Kutta finite volume method for numerically solving convection and convection-diffusion equations. Eulerian-Lagrangian and semi-Lagrangian methods have grown in popularity mostly due to their…

In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A mathematically exact…

In this work, we discuss some points relevant for stochastic modelling of one- and two-phase turbulent flows. In the framework of stochastic modelling, also referred to PDF approach, we propose a new Langevin model including all viscosity…

In the Eulerian approach, the motion of an incompressible fluid is usually described by the velocity field which is given by the Navier--Stokes system. The velocity field generates a flow in the space of volume-preserving diffeomorphisms.…

The numerical solution of the Stokes equations on an evolving domain with a moving boundary is studied based on the arbitrary Lagrangian-Eulerian finite element method and a second-order projection method along the trajectories of the…

We present three-dimensional direct numerical simulations of turbulent Rayleigh-B\'enard convection (RBC) in the Lagrangian frame of reference for Rayleigh numbers $10^5 \leq Ra \leq 10^{10}$ and a Prandtl number $Pr=0.7$ in a plane layer…

Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that…

We present high-resolution direct numerical simulations of turbulent three-dimensional Rayleigh-Benard convection with a focus on the Lagrangian properties of the flow. The volume is a Cartesian slab with an aspect ratio of four bounded by…

We introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when…

Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away…

Recent developments in vortex particle methods for simulating three-dimensional incompressible flows are presented. A lightweight, dynamic Large-Eddy Simulation model is tested, featuring a dynamic procedure that relies solely on Lagrangian…

Recent advances in random-walk particle-tracking have enabled direct simulation of mixing and reactions on particles by allowing the particles to interact with each other using a multi-point mass transfer scheme. The mass transfer scheme…