Related papers: Error estimates for the highly efficient and energ…
A rotation-two-component Camassa-Holm (R2CH) system was proposed recently to describe the motion of shallow water waves under the influence of gravity. This is a highly nonlinear and strongly coupled system of partial differential…
Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and…
This paper presents a global stability result on perturbations near a background magnetic field to the 2D incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion on the periodic domain. The stability result provides…
We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is…
In this paper, we present an efficient energy stable scheme to solve a phase field model incorporating contact line condition. Instead of the usually used Cahn-Hilliard type phase equation, we adopt the Allen-Cahn type phase field model…
We introduce a family of bi-grid schemes in finite elements for solving 2D incompressible Navier-Stokes equations in velocity and pressure $(u,p)$. The new schemes are based on projection methods and use two pairs of FEM spaces, a sparse…
In this paper, we present an error estimate of a second-order linearized finite element (FE) method for the 2D Navier-Stokes equations with variable density. In order to get error estimates, we first introduce an equivalent form of the…
In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and…
We discuss a class of magnetic-electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a key $L^{3}$ estimate for divergence-free finite element…
The ideal MHD equations are a central model in astrophysics, and their solution relies upon stable numerical schemes. We present an implementation of a new method, which possesses excellent stability properties. Numerical tests demonstrate…
Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
A well-balanced second order finite volume central scheme for the magnetohydrodynamic (MHD) equations with gravitational source term is developed in this paper. The scheme is an unstaggered central scheme that evolves the numerical solution…
We present a new computational method for smoothly matching general relativistic ideal magnetohydrodynamics (MHD) to its force-free limit. The method is based on a flux-conservative formalism for MHD and its force-free limit, and a vector…
Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable…
We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is based on two key ideas: the integration during the time-steps of…
We construct and analyze a projection-free linearly implicit method for the approximation of flows of harmonic maps into spheres. The proposed method is unconditionally energy stable and, under a sharp discrete regularity condition,…
We are concerned in designing a suitable numerical scheme based on the equal-order hybrid high-order (HHO) method for the linear parabolic integro-differential equations. The spatial discretization is made using the equal-order HHO method…
This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we have established the stability theory and proposed stability conditions based on the delta dissipativity. In Part…
We show that the one-dimensional (1D) two-fluid model (TFM) for stratified flow in channels and pipes (in its incompressible, isothermal form) satisfies an energy conservation equation, which arises naturally from the mass and momentum…