相关论文: A Performance Study of Horizontally Explicit Verti…

In this paper, we propose a new high order semi-implicit scheme for the all Mach full Euler equations of gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL restrictions…

The residual-based variational multiscale (VMS) formulation has achieved remarkable success in large-eddy simulation of turbulent flows. However, its temporal discretization has largely remained limited to second-order implicit schemes. The…

This study addresses the critical challenge of error accumulation in spatio-temporal auto-regressive (AR) predictions within scientific machine learning models by exploring temporal integration schemes and adaptive multi-step rollout…

We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and…

This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive…

In this paper we develop the James - Stein improved estimation method for a nonparametric periodic function observed with the Levy noises in continuous time. An adaptive model selection procedure based on the improved weighted least square…

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…

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…

To solve the Cahn-Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the…

Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and…

Segregated Runge-Kutta (SRK) schemes are time integration methods for the incompressible Navier-Stokes equations. In this approach, convection and diffusion can be independently treated either explicitly or implicitly, which in particular…

We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using…

Efficient time integration methods based on operator splitting are introduced for the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as mathematical model for the propagation of sound waves in high…

We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations discretized on staggered (MAC) grids. The scheme is based on finite difference approximations…

Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…

In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…

We develop an efficient, unconditionally stable, variable step second order exponential time differencing scheme for the incompressible Navier Stokes equations in two and three spatial dimensions under periodic boundary conditions, together…

We propose a novel family of asymptotically stable, implicit-explicit, adaptive, time integration method (denoted with the $\theta$-method) for the solution of the fractional advection-diffusion-reaction (FADR) equations. This family of…

This work aims to model the hypersurface of the effective elastic modulus, \( E_{z, \text{eff}} \), and thickness, \( th_{\text{eff}} \), in corrugated boards. A Latin Hypercube Sampling (LHS) is followed by Gaussian Process Regression…

Splitting is a method to handle application problems by splitting physics, scales, domain, and so on. Many splitting algorithms have been designed for efficient temporal discretization. In this paper, our goal is to use temporal splitting…