相关论文: Lagrangian, Game Theoretic and PDE Methods for Ave…

We study front speeds of curvature and strain G-equations arising in turbulent combustion. These G-equations are Hamilton-Jacobi type level set partial differential equations (PDEs) with non-coercive Hamiltonians and degenerate nonlinear…

G-equation is a popular level set model in turbulent combustion, and becomes an advective mean curvature type evolution equation when curvature of a moving flame in a fluid flow is considered: $$ G_t + \left(1-d\,…

We perform a computationl study of front speeds of G-equation models in time dependent cellular flows. The G-equations arise in premixed turbulent combustion, and are Hamilton-Jacobi type level set partial differential equations (PDEs). The…

Lagrangian averaging plays an important role in the analysis of wave--mean-flow interactions and other multiscale fluid phenomena. The numerical computation of Lagrangian means, e.g. from simulation data, is however challenging. Typical…

We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection…

The modelling of fluid particle accelerations in homogeneous, isotropic turbulence in terms of second-order stochastic models for the Lagrangian velocity is considered. The basis for the Reynolds model (A. M. Reynolds, \textit{Phys. Rev.…

The G-equation is a popular model for premixed turbulent combustion. Mathematically it has attracted a lot of interest in part because it is a simple example of a Hamilton-Jacobi equation which is only coercive `on average'. This paper…

The Lagrangian probability-density-function model, proposed in Part I for dense particle-laden turbulent flows, is validated here against Eulerian-Lagrangian direct numerical simulation (EL) data for different homogeneous flows, namely…

This paper provides a rigorous convergence rate and complexity analysis for a recently introduced framework, called PDE acceleration, for solving problems in the calculus of variations, and explores applications to obstacle problems. PDE…

Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently,…

Turbulence is prevalent in nature and industry, from large-scale wave dynamics to small-scale combustion nozzle sprays. In addition to the multi-scale nonlinear complexity and both randomness and coherent structures in its dynamics,…

High Reynolds Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of…

Modeling statistical properties of motion of a Lagrangian particle advected by a high-Reynolds-number flow is of much practical interest and complement traditional studies of turbulence made in Eulerian framework. The strong and nonlocal…

We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. For a fluid velocity field that is…

Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…

G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level…

Predicting turbulent flame speed (the large time front speed) is a fundamental problem in turbulent combustion theory. Several models have been proposed to study the turbulent flame speed, such as the G-equations, the F-equations…

Most approaches in Lagrangian fluid dynamics simulations proceed from the definition of particle volumes, from which discrete versions of the spatial differential operators are derived. Recently, Gallou\"et and M\'erigot [1] simultaneously…

Hyperbolic partial differential equations (PDEs) cover a wide range of interesting phenomena, from human and hearth-sciences up to astrophysics: this unavoidably requires the treatment of many space and time scales in order to describe at…

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…