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A semi-implicit three-dimensional numerical model for non-hydrostatic pressure free-surface flows on an unstructured,sigma grid

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International Journal of Sediment Research 2013年第1期28卷 77-89页

作者： De-chao HU De-yu ZHONG Guang-qian WANG Yong-hui ZHU Senior Engineer Yangtze River Scientific Research InstituteWuhan 430010China Senior Engineer Yangtze River Scientific Research Institute State Key Laboratory of Hydroscience and Engineering Tsinghua University Associate Professor State Key Laboratory of Hydroscience and EngineeringTsinghua University

A semi-implicit 3-D numerical formulation for solving non-hydrostatic pressure free-surface flows on an unstructured,sigma grid is proposed.Pressure-splitting and 9 semi-implicit methods are inherited and reformed from Casulli’s z-coordinate formulation.The non-orthogonal sigma-coordinate transformation leads to additional terms. The resulting linear system for the non-hydrostatic correction is diagonally dominant but unsymmetric,and it is solved by the BiCGstab method.In contrast with z-coordinate non-hydrostatic models,the new model fits vertical boundaries much better,which is important for the long-time simulation of sediment transport and riverbed deformation.A lock-exchange density flow is computed to determine whether the new scheme is able to simulate non-hydrostatic free-surface flows.The new model is further verified using the field data of a natural river bend of the lower Yangtze River.Good agreement between simulations and earlier research results,field data is obtained, indicating that the new model is applicable to hydraulic projects in real rivers.

关键词： Three-dimensional Non-hydrostatic pressure semi-implicit Sigma-coordinate Unstructured grid

A three-dimensional semi-implicit unstructured grid finite volume ocean model

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Acta Oceanologica Sinica 2013年第1期32卷 68-78页

作者： WANG Zhili GENG Yanfen State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Nanjing Hydraulic Research Institute School of Transportation Southeast University

A new three-dimensional semi-implicit finite-volume ocean model has been developed for simulating the coastal ocean circulation, which is based on the staggered C-unstructured non-orthogonal grid in the hor- izontal direction and z-level grid in the vertical direction. The three-dimensional model is discretized by the semi-implicit finite-volume method, in that the free-surface and the vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly by an integral method. The partial cell method is used for resolving topography, which enables the model to better represent irregular topography. The model has been tested against analytical cases for wind and tidal oscillation circulation, and is applied to simulating the tidal flow in the Bohal Sea. The results are in good agreement both with the analytical solutions and measurement results.

关键词： three-dimensional model finite volume unstructured grid semi-implicit z-level grid

A FINITE VOLUME semi-implicit semi-LAGRANGIAN SCHEME ON THE YIN-YANG MESH

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Journal of Tropical Meteorology 2019年第3期25卷 373-384页

作者：刘宇迪李大伟 Institute of Meteorology and Oceanography National University of Defense Technology

Designed for grid point systems, the traditional semi-Lagrangian semi-implicit scheme is not mass-conserving and can lead to significant solution errors. In the present study, a finite-volume semi-Lagrangian semi-implicit scheme(hereafter 'FVSLSI') is designed for the Yin-Yang mesh and tested in a barotropic shallow water model in the spherical coordinate system. Three test cases, i.e. the advection of a solid body, a steady state nonlinear zonal geostrophic flow and the deformation flow, are simulated to compare the performance of the FVSLSI with that of the traditional semi-Lagrangian scheme(hereafter 'SL') from perspectives of shape preservation, mass conservation,normalized bias, and convergence rate. Results indicate that the FVSLSI performs better than the SL in mass conservation and shape preservation. The bias by the FVSLSI is smaller than that by the SL, while the rate of convergence by the FVSLSI is larger than that by the SL. The FVSLSI also allows large time step. Therefore, the FVSLSI is suggested to be distributed to communities that are developing atmospheric/oceanic models.

关键词： semi-implicit scheme semi-Lagrangian scheme mass-conservative scheme Yin-Yang mesh finite volume

THE FORMULATION OF A PERFECT SQUARE CONSERVATIVE semi-implicit TIME DIFFERENCE SCHEME AND ITS PRELIMINARY CHECK

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Chinese Science Bulletin 1992年第6期37卷 497-502页

作者：钟青 Institute of Atmospheric Physics Academia Sinica Beijing 100080 PRC

Quantitative studies of scientific problems require solving correspondent mathematical models. Although a great deal of mathematical models of evolutional problems are set up under continuous space-time meaning, they usually had to be solved numerically after space-time discretization because nonlinear mathematical models except some

关键词： nonlinear semi-implicit perfecr square conservative time difference scheme computational finstability computational accuracy

AN IMPROVED semi-implicit TIME DIFFERENCE SCHEME OF SPECTRAL MODEL AND NUMERICAL APPLICATIONS

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Acta meteorologica Sinica 2002年第2期16卷 180-194页

作者：张朝林 ***. 郑庆林宋青丽 Dr.ZHANG Chaolin Beijing Urban Meteorological Research InstituteBeijing Meteorological BureauNo.44 Zizhuyuan Road.Haidian District.Beijing 100089P.R.ChinaPhone:(86)-010-68414488-6276.E-mail:c_lzhang Chinese Academy of Meteorological Sciences Beijing 100081

In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and external-gravity waves in the atmospheric forecasting equation. Additionally,due to using time difference on two terms at different time.the popular scheme artificially introduces unbalance between pressure gradient force and Coriolis force terms while numerically computing their small difference between large quantities.According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation,one improved semi-implicit time difference scheme is also designed in our study.By adopting a kind of revised time-explicit-difference scheme to these linear terms that still included in spectral model governing equations,the defect of spectral model which only partly using semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectral coefficients of prognostic equations,especially of Helmholtz divergence equation,can be worked out without any numerical iteration,the time-step (computation stability) can also be enlarged (enhanced) by properly introducing an adjustable coefficient.

关键词： spectral model semi-implicit time difference scheme numerical experiment computational stability

Revisit of semi-implicit Schemes for Phase-Field Equations

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Analysis in Theory and Applications 2020年第3期36卷 235-242页

作者： Tao Tang Division of Science and Technology BNU-HKBU United International CollegeZhuhaiGuangdong 519087China SUSTech International Center for Mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China

It is a very common practice to use semi-implicit schemes in various computations,which treat selected linear terms implicitly and the nonlinear terms explicitly.For phase-field equations,the principal elliptic operator is treated implicitly to reduce the associated stability constraints while the nonlinear terms are still treated explicitly to avoid the expensive process of solving nonlinear equations at each time step.However,very few recent numerical analysis is relevant to semi-implicit schemes,while”stabilized”schemes have become very popular.In this work,we will consider semiimplicit schemes for the Allen-Cahn equation with general potential function.It will be demonstrated that the maximum principle is valid and the energy stability also holds for the numerical solutions.This paper extends the result of Tang&Yang(J.Comput.Math.,34(5)(2016),pp.471–481),which studies the semi-implicit scheme for the Allen-Cahn equation with polynomial potentials.

关键词： semi-implicit phased-field equation energy dissipation maximum principle.

Stability of semi-implicit Finite Volume Scheme for Level Set Like Equation

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Communications in Mathematical Research 2015年第4期31卷 351-361页

作者： Kim Kwang-il Son Yong-chol Ma Fu-ming School of Mathematics Jilin University Department of Mathematics University of Science

We study numerical methods for level set like equations arising in image processing and curve evolution problems. semi-implicit finite volume-element type schemes are constructed for the general level set like equation （image selective smoothing model） given by Alvarez et al. （Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29： 845-866）. Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in L∞ and W1＇2 （W1＇1） sense in isotropic （anisotropic） diffu- sion domain.

关键词： level set like equation semi-implicit finite volume scheme stability

An improved semi-implicit direct kinetics method for transient analysis of nuclear reactors

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Nuclear Science and Techniques 2019年第11期30卷 108-126页

作者： Roozbeh Vadi Kamran Sepanloo School of Nuclear Reactors and Safety Nuclear Science and Technology Research Institute

semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantity for the fission source term in the delayed neutron differential equations.Hence,these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained,which leads to a significant reduction in computational cost.As the fission source is not known in a time step,the original study suggested using a constant quantity pertaining to the previous time step for this purpose,and a reduction in the size of the time step was proposed to lessen the imposed errors.However,this remedy notably diminishes the main advantage of the SIDK method.We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications,the mentioned drawbacks will be mitigated adequately.To test this idea,a novel multigroup,multi-dimensional diffusion code using the finitevolume method and a point-implicit solver is developed which works in both transient and steady states.In addition to the SIDK,two other kinetic methods,i.e.,direct kinetics and higher-order backward discretization,are programmed into the diffusion code for comparison with the proposed model.The final code is tested at different conditions of two well-known transient benchmark problems.Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods,it reduces the total time required for computation by up to 24%.

关键词： Nuclear kinetics semi-implicit direct kinetics Higher-order backward discretization Finite volume Point-implicit solver

A semi-implicit Scheme of Lattice Boltzmann Method for Two Dimensional Cavity Flow Simulation

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Open Journal of Fluid Dynamics 2015年第1期5卷 10-16页

作者： Lei Zhang Jun Yao Hai Sun Jianguang Zhang School of Petroleum Engineering China University of Petroleum Qingdao China School of Geosciences China University of Petroleum Qingdao China

The calculation sequence of collision, propagation and macroscopic variables is not very clear in lattice Boltzmann method (LBM) code implementation. According to the definition, three steps should be computed on all nodes respectively, which mean three loops are needed. While the “pull” scheme makes the only one loop possible for coding, this is called semi-implicit scheme in this study. The accuracy and efficiency of semi-implicit scheme are discussed in detail through the simulation of lid-driven cavity flow. Non-equilibrium extrapolation scheme is adopted on the boundary of simulation area. The results are compared with two classic articles, which show that semi-implicit scheme has good agreement with the classic scheme. When Re is less than 3000, the iterations steps of semi-scheme can be decreased by about 30% though comparing the semi-implicit scheme with standard scheme containing three loops. As the Re increases into more than 3400, the standard scheme is not converged. On the contrary, the iterations of semi-implicit scheme are approximately linear to Re.

关键词： Lattice Boltzmann Cavity Flow Reynolds Number semi-implicit