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The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete…
We address the formulation and analysis of energy and momentum conserving time integration schemes in the context of particle dynamics, and in particular atomic systems. The article identifies three critical aspects of these models that…
We present an explicit temporal discretization of particle-in-cell schemes for the Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple,…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
On this paper, we have proposed an approach to observe the time-centered difference scheme for dissipative mechanical systems from a Hamiltonian perspective and to introduce the idea of symplectic algorithm to dissipative systems. The…
This paper introduces a robust reformulation of the incompressible Navier-Stokes equations, establishing a foundational framework for designing efficient, structure-preserving algorithms that strictly conserve the original energy…
In this paper, energy-preserving methods are formulated and studied for solving charged-particle dynamics. We first formulate the scheme of energy-preserving methods and analyze its basic properties including algebraic order and symmetry.…
Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature…
We study numerical methods for porous media equation (PME). There are two important characteristics: the finite speed propagation of the free boundary and the potential waiting time, which make the problem not easy to handle. Based on…
The traditional explicit electrostatic momentum-conserving Particle-in-cell algorithm requires strict resolution of the electron Debye length to deliver numerical accuracy. The explicit electrostatic energy-conserving Particle-in-Cell…
This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…
The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the…
Achieving large-scale kinetic modelling is a crucial task for the development and optimization of modern plasma devices. With the trend of decreasing pressure in applications such as plasma etching, kinetic simulations are necessary to…
In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager…
We study by means of numerical simulations the model of dissipative particle dynamics with energy conservation for the simple case of thermal conduction. It is shown that the model displays correct equilibrium fluctuations and reproduces…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. We have studied numerical methods for PME by an energetic variational approach in [C. Duan et al, J. Comput. Phys., 385 (2019) 13-32], where the…