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An unconditionally positivity-preserving implicit-explicit scheme for evolutionary stable distribution model

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2022年第0期403卷 113883-113883页

作者： Zhang, Chun-Hua Chen, Guang-Ze Fang, Zhi-Wei Lin, Xue-lei Sun, Hai-Wei Nanchang Hangkong Univ Coll Math & Informat Sci Nanchang 330063 Jiangxi Peoples R China Univ Macau Dept Math Macau Peoples R China Hong Kong Baptist Univ Dept Math Hong Kong Peoples R China

In this paper, we study the numerical solution for the evolutionary stable distribution (ESD) model. A new implicit-explicit scheme is proposed to discretize the ESD model, which can keep the numerical solution unconditionally positive at each time step. Moreover, it is theoretically proved that the proposed scheme satisfies the property of the entropy dissipation. Numerical experiments are carried out to demonstrate the numerical accuracy and the effectiveness of the proposed scheme. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Evolutionary stable distribution implicit-explicit scheme Positivity-preserving Entropy dissipation

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Numerical simulation of a compressible two-layer model: A first attempt with an implicit-explicit splitting scheme

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2019年 346卷 357-377页

作者： Demay, Charles Bourdarias, Christian de Meux, Benoit de laage Gerbi, Stephane Herard, Jean-Marc EDF R&D 6 Quai Watier F-78401 Chatou France CNRS UMR 5127 Lab Math F-73376 Le Bourget Du Lac France Univ Savoie Mt Blanc F-73376 Le Bourget Du Lac France Univ Aix Marseille CNRS UMR 7373 Inst Math Marseille F-13453 Marseille France Cent Marseille F-13453 Marseille France

This paper is devoted to the numerical simulation of the compressible two-layer model developed in Demay and Herard (2017). The latter is a hyperbolic two-fluid two-pressure model dedicated to gas-liquid flows in pipes, especially stratified air-water flows. Using explicit schemes, one obtains a CFL condition based on the celerity of (fast) acoustic waves which typically brings large numerical diffusivity for the (slow) material waves and small time steps. In order to overcome these drawbacks, the proposed scheme involves an operator splitting and an implicit-explicit time discretization. Thus, the full system is split into two hyperbolic sub-systems. The first one deals with the transport equation on the liquid height using an explicit scheme and upwind fluxes. The second one deals with the averaged mass and momentum conservation equations of both phases using an implicit scheme which handles the propagation of acoustic waves. At last, the positivity of heights and densities is ensured under a CFL condition which involves material velocities. Numerical experiments are performed using acoustic as well as material time steps. Adding the Rusanov scheme for comparison, the best accuracy is obtained with the proposed scheme used with acoustic time steps. Focusing on material waves of the convective system, the efficiency of the latter is improved when using material steps. However, considering the whole system with relaxation source terms, an efficient approximation of slow dynamics, typically a gravity driven flow, is still challenging. (C) 2018 Elsevier B.V. All rights reserved.

关键词： implicit-explicit scheme Operator splitting Two-layer model Gas-liquid flows

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A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrodinger equations

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NUMERICAL ALGORITHMS 2017年第1期75卷 147-172页

作者： Khaliq, A. Q. M. Liang, X. Furati, K. M. Middle Tennessee State Univ Dept Math Sci Murfreesboro TN 37132 USA Middle Tennessee State Univ Ctr Computat Sci Murfreesboro TN 37132 USA Hubei Univ Arts & Sci Dept Informat & Comp Sci Xiangyang 441053 Hubei Peoples R China King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

A fourth-order implicit-explicit time-discretization scheme based on the exponential time differencing approach with a fourth-order compact scheme in space is proposed for space fractional nonlinear Schrodinger equations. The stability and convergence of the compact scheme are discussed. It is shown that the compact scheme is fourth-order convergent in space and in time. Numerical experiments are performed on single and coupled systems of two and four fractional nonlinear Schrodinger equations. The results demonstrate accuracy, efficiency, and reliability of the scheme. A linearly implicit conservative method with the fourth-order compact scheme in space is also considered and used on the system of space fractional nonlinear Schrodinger equations.

关键词： Space fractional nonlinear Schrodinger equations Riesz fractional derivative implicit-explicit scheme Compact scheme Exponential time differencing

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implicit-explicit scheme FOR THE ALLEN-CAHN EQUATION PRESERVES THE MAXIMUM PRINCIPLE

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Journal of Computational Mathematics 2016年第5期34卷 451-461页

作者： Tao Tang Jiang Yang Department of Mathematics Southern University of Science and Technology Shenzhen Guangdong 518055 China Department of Applied Mathematics Columbia University New York NY 10027 USA

It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes？ To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-explicit discretization in time and central finite difference in space. In other words, this commonly used numerical method for the Allen-Cahn equation preserves the maximum principle.

关键词： Allen-Cahn Equations implicit-explicit scheme Maximum principle Nonlin-ear energy stability.

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A high-order implicit-explicit Runge-Kutta type scheme for the numerical solution of the Kuramoto-Sivashinsky equation

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2021年第6期98卷 1254-1273页

作者： Bhatt, H. P. Chowdhury, A. Utah Valley Univ Dept Math Orem UT 84058 USA Savannah State Univ Dept Math Savannah GA USA

This manuscript is concerned with the development and the implementation of a numerical scheme to study the spatio-temporal solution profile of the well-known Kuramoto-Sivashinsky equation with appropriate initial and boundary conditions. A fourth-order Runge-Kutta based implicit-explicit scheme in time along with compact higher-order finite difference scheme in space is introduced. The proposed scheme takes full advantage of the method of line (MOL) and partial fraction decomposition techniques, therefore, it just needs to solve two backward Euler-type linear systems at each time step to get the solution. Performance of the scheme is investigated by testing it on some test examples and by comparing numerical results with relevant known schemes. The numerical results showed that the proposed scheme is more accurate and reliable than existing schemes to solve Kuramoto-Sivashinsky equation.

关键词： implicit-explicit scheme Kuramoto-Sivashinsky equation partial fraction splitting technique compact finite difference exponential time differencing 65

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An implicit-explicit Local Discontinuous Galerkin scheme for Analysis of Organic Electrochemical Transistors

An Implicit-Explicit Local Discontinuous Galerkin Scheme for...

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International Symposium of the Applied-Computational-Electromagnetics-Society (ACES)

作者： Dong, Ming Chen, Liang Bagci, Hakan King Abdullah Univ Sci & Technol KAUST Div Comp Elect & Math Sci & Engn CEMSE Thuwal 239556900 Saudi Arabia

ISBN: (纸本)9781733509626

In this paper, an implicit-explicit (IMEX) local discontinuous Galerkin (LDG) method is proposed to analyze the organic electrochemical transistors (OECTs). The LDG method is used to spatially discretize the coupled system of Poisson and drift-diffusion (DD) equations. For the time integration, the IMEX scheme uses implicit and explicit methods for the linear diffusion and the nonlinearly coupled drift terms, respectively. This results in a time marching scheme where the time-step size is upper-bounded by a positive constant but can be selected independently from spatial mesh size. Numerical results demonstrate that the proposed IMEX-LDG scheme allows for a significantly larger time-step size than its fully-explicit counterpart, and therefore much faster in simulation of OECTs.

关键词： drift-diffusion (DD) model implicit-explicit scheme local discontinuous Galerkin (LDG) method organic electrochemical transistor (OECT)

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Non-conservative Godunov-type schemes: Application to two-phase flows with surface tension using Lagrange-transport splitting strategy

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JOURNAL OF COMPUTATIONAL PHYSICS 2025年 532卷

作者： Tallois, Lucas Peluchon, Simon Gallice, Gerard Villedieu, Philippe CEA CESTA 15 Ave SablieresCS 60001 F-33116 Le Barp France INSA 135 Ave Rangueil F-31400 Toulouse France Univ Toulouse DMPE ONERA F-31000 Toulouse France

This paper aims to present one-dimensional and multi-dimensional non-conservative Godunovtype schemes in a general framework. These schemes are designed to preserve equilibrium solutions discretely. Gallice's theory of simple solvers is used to solve the Riemann problem approximately. These numerical schemes are applied to compute two-phase flows with surface tension effects. Time integration is based on the Lagrange-Transport splitting strategy, allowing to solve the acoustic waves with an implicit time scheme.

关键词： Godunov-type scheme Surface tension Two-phase flows Riemann solver implicit-explicit scheme

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Uniform error analysis of an exponential IMEX-SAV method for the incompressible flows with large Reynolds number based on grad-div stabilization

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2025年 140卷

作者： An, Rong Wan, Weiwen Wenzhou Univ Coll Math & Phys Wenzhou 325035 Peoples R China

Based on the grad-div stabilization and scalar auxiliary variable (SAV) methods, a first-order Euler implicit/explicit finite element scheme is studied for the Navier-Stokes equations with large Reynolds number. In the designing of numerical scheme, the nonlinear term is explicitly treated such that one only needs to solve a constant coefficient algebraic system at each time step. Meanwhile, the proposed scheme is unconditionally stable without any condition of the time step a and mesh size h . In finite element discretization, we use the stable Taylor-Hood element for the approximation of the velocity and pressure. By a rigorous analysis, we derive an uniform L2 2 error estimate O ( a + h 2 ) of the velocity in which the constant is independent of the viscosity coefficient. Finally, numerical experiments are given to support theoretical results and the efficiency of the proposed scheme.

关键词： Navier-Stokes equations Scalar auxiliary variable method Grad-div stabilization implicit-explicit scheme Uniform error estimate

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Efficient and long time stable IMEX schemes for the unsteady dual-porosity-Stokes system

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MATHEMATICS AND COMPUTERS IN SIMULATION 2025年 236卷 111-134页

作者： Li, Yi Li, Ning Xue, Dandan Qin, Yi Northwest Univ Sch Math Xian 710127 Shaanxi Peoples R China Northwest Univ Shaanxi Key Lab Math Theory & Computat Fluid Mech Xian 710127 Shaanxi Peoples R China Henan Agr Univ Coll Informat & Management Sci Zhengzhou 450002 Peoples R China Chengdu Univ Technol Coll Math & Phys Chengdu 610059 Sichuan Peoples R China Shaanxi Univ Sci & Technol Sch Math & Data Sci Xian 710021 Shaanxi Peoples R China

In this paper, we introduce an efficient and long time stable implicit-explicit(IMEX) scheme for the dual-porosity-Stokes equations. On the basis of backward Euler scheme and the solution at previous time level, we apply implicit discretization for sub-problems terms and explicit discretization for interface terms. By introducing a new scalar auxiliary variable (SAV), the scheme avoids time step constraints in long time stability analysis. We derive the error estimates of the full discretization with finite element method for the spatial discretization without any time step conditions. Moreover, we extend the approach to higher order IMEX schemes and develop variable time stepsize adaptive algorithm using time filter. Numerical tests are provided to validate the accuracy of several numerical schemes and assess industrial applicability of the coupled model in the multistage fractured horizontal wellbore problem.

关键词： implicit-explicit scheme Scalar auxiliary variable Dual-porosity-Stokes Long time stability Error estimates Multistage fractured horizontal wellbore

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Numerical-Analytical Method for the Burgers Equation with a Periodic Boundary Condition

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Journal of Mathematical Sciences (United States) 2024年第3期285卷 301-315页

作者： Bezrodnykh, S.I. Pikulin, S.V. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences Moscow Russian Federation

We construct an efficient numerical-analytical method for solving the initial-boundary value problem for the Burgers equation on a segment with a periodic boundary condition. The method includes the reduction to a linear problem based on an implicit-explicit time discretization scheme and an analytical solution of an auxiliary linear problem at each time step using the explicit form of the corresponding Green’s function. The efficiency of the constructed method is due to the fact that the algorithm for solving the auxiliary problem has only linear complexity in terms of the number of spatial discretization nodes used, without involving difference approximations of the derivatives of the desired function. On the basis of the Cole–Hopf substitution, we obtain an explicit periodic solution of the problem on the interval and compare the results of the numerical implementation of the constructed algorithm with this explicit solution. The developed method demonstrated a combination of high computational efficiency and accuracy of the result. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

关键词： Burgers equation Green’s function implicit-explicit scheme numerical-analytical method

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