Related papers: An explicit pseudo-energy conserving time-integrat…
A new conservative symmetry-preserving second-order time-accurate PISO-based pressure-velocity coupling for solving the incompressible Navier-Stokes equations on unstructured collocated grids is presented in this paper. This new method for…
Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…
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,…
We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier- Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection…
Adaptive precision molecular dynamics simulations have developed along energy- and force-coupling approaches, which allow for a continuous transition between different particle descriptions or interaction potentials. Most approaches…
We focus on the numerical approximation of the Cahn-Hilliard type equations, and present a family of second-order unconditionally energy-stable schemes. By reformulating the equation into an equivalent system employing a scalar auxiliary…
High order energy-preserving methods for Hamiltonian systems are presented. For this aim, an energy-preserving condition of continuous stage Runge--Kutta methods is proved. Order conditions are simplified and parallelizable conditions are…
Maintaining conservation laws in the fully discrete setting is critical for accurate long-time behavior of numerical simulations and requires accounting for discrete conservation properties in both space and time. This paper derives…
This paper introduces a novel second-order splitting scheme for charged-particle dynamics in strong magnetic fields characterized by the maximal ordering. The proposed scheme is explicit and symmetric, which respectively ensure the…
We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolation of the state and we approximate the action in a small…
An implicit variable-step BDF2 scheme is established for solving the space fractional Cahn-Hilliard equation, involving the fractional Laplacian, derived from a gradient flow in the negative order Sobolev space $H^{-\alpha}$,…
Elegant integration schemes of second and fourth order for simulations of rigid body systems are presented which treat translational and rotational motion on the same footing. This is made possible by a recent implementation of the exact…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
We describe a new algorithm for the integration of self-gravitating fluid systems using SPH method. We split the Hamiltonian of a self-gravitating fluid system to the gravitational potential and others (kinetic and internal energies) and…
We perform simulations of feedback from supernovae and black holes with smoothed particle hydrodynamics (SPH). Such strong perturbations are inaccurately handled with standard time integration schemes, leading to poor energy conservation, a…
In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system…
Using a recent characterization of energy-preserving B-series, we derive the explicit conditions on the coefficients of a Runge-Kutta method that ensure energy preservation (for Hamiltonian systems) up to a given order in the step size,…
The single-step explicit time integration methods have long been valuable for solving large-scale nonlinear structural dynamic problems, classified into single-solve and multi-sub-step approaches. However, no existing explicit single-solve…
In this paper, the emergence of macroscopic-scale pseudo time-irreversibility is studied in the closed classical many-body system of pair interacting particles. First, exact continuum equations are derived to the Hamiltonian dynamics…
Simulation of many-particle system evolution by molecular dynamics takes to decrease integration step to provide numerical scheme stability on the sufficiently large time interval. It leads to a significant increase of the volume of…