相关论文: New limiter regions for multidimensional flows

In the present paper we study the fast rotation limit for viscous incompressible fluids with variable density, whose motion is influenced by the Coriolis force. We restrict our analysis to two dimensional flows. In the case when the initial…

This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…

We present stability and error analysis for algebraic flux correction schemes based on monolithic convex limiting. For a continuous finite element discretization of the time-dependent advection equation, we prove global-in-time existence…

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by…

The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection-diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear…

In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the…

This paper is the first part of our series work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, both drift and diffusion terms may contain the control variable but the control region…

In the paper we extend the Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) model proposed in [Europhys. Lett. \textbf{90}, 54003 (2010)] so that it is suitable also for incompressible flows. To decrease the artificial oscillations,…

We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a…

The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with…

We study the existence of weak solutions to the two-phase model of crowd motion. The model encompasses the flow in the uncongested regime (compressible) and the congested one (incompressible) with the free boundary separating the two…

Conservation laws are usually studied in the context of sufficient regularity conditions imposed on the flux function, usually $C^{2}$ and uniform convexity. Some results are proven with the aid of variational methods and a unique minimizer…

Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the…

We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…

We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…

We present a set of effective outflow/open boundary conditions and an associated algorithm for simulating the dynamics of multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids in domains involving outflows or…

Incompressibility is a fundamental condition in most fluid models. Accumulation of simulation errors violates it and causes volume loss. Past work suggested correction methods to battle it. These methods, however, are imperfect and in some…

We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an $H(\mathrm{div})$-conforming space,…

We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary controls, for the velocity vector and angular velocity of rotation…

Semilinear parabolic systems with bi-linear nonlinearities cover a lot of applications and their optimal control leads to relatively simple optimality conditions. An example is the incompressible Navier-Stokes system for homogeneous fluids,…