相关论文: Numerical computation of triangular cavity flows b…
We present a Lagrange--Galerkin scheme free from numerical quadrature for the Navier--Stokes equations. Our idea is to use a locally linearized velocity and the backward Euler method in finding the position of fluid particle at the previous…
We present a Lagrange-Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange-Galerkin…
Numerical solutions of 2-D steady incompressible flow inside a triangular cavity are presented. For the purpose of comparing our results with several different triangular cavity studies with different triangle geometries, a general triangle…
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…
We propose and analyze a pressure-stabilized projection Lagrange--Galerkin scheme for the transient Oseen problem. The proposed scheme inherits the following advantages from the projection Lagrange--Galerkin scheme. The first advantage is…
We apply the Local Discontinuous Galerkin discretisation to flow equations of the O(N)-model in the Local Potential Approximation. The improved stability is directly observed by solving the flow equation for various $N$ and space-time…
We consider a pressure-stabilized Lagrange-Galerkin scheme for the transient Oseen problem with small viscosity. In the scheme we use the equal-order approximation of order $k$ for both the velocity and pressure, and add a symmetric…
A numerical model and parallel software for 3D simulations of granular flows have been developed based on the Lagrangian particle (LP) method [R.Samulyak, X. Wang, H.-C. Chen, Lagrangian particle method for compressible fluid dynamics, J.…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…
A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the…
Error estimates with optimal convergence orders are proved for a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations. The scheme is a combination of Lagrange-Galerkin method and Brezzi-Pitkaranta's stabilization method. It…
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…
We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both…
Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by…
A new high order accurate semi-implicit space-time Discontinuous Galerkin method on staggered grids, for the simulation of viscous incompressible flows on two-dimensional domains is presented. The designed scheme is of the Arbitrary…
We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…
Anomalous diffusions are ubiquitous in nature, whose functional distributions are governed by the backward Feynman-Kac equation. In this paper, the local discontinuous Galerkin (LDG) method is used to solve the 2D backward Feynman-Kac…
Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study…
We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with the Lagrangian multiplier approach. They are as efficient…