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Scheme using a finite-volume method for local horizontal derivatives in the spectral model: The non-hydrostatic case

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QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY 2024年第765期150卷 4987-4999页

作者： Yang, Jinhui Wu, Jianping Song, Junqiang Peng, Jun Yin, Fukang Leng, Hongze Ren, Kaijun Yang, Xiangrong Natl Univ Def Technol Coll Meteorol & Oceanog Changsha Peoples R China

In a typical non-hydrostatic spectral dynamic numerical weather prediction (NWP) kernel, all forecast variables are transformed between grid point and spectral spaces to compute their gradients and solve the implicit problem. This kernel requires numerous spectral transformations, which depend heavily on extensive global communication and significantly hinder parallel computing efficiency. This paper introduces an innovative non-hydrostatic spectral kernel that incorporates a finite-volume method within the spectral framework. We have developed a horizontal divergence (D)-based structure equation, allowing direct computation of most prognostic variables and their horizontal gradients at grid point space. By doing so, the need for spectral transformations is substantially decreased. Our experiments demonstrate that this new approach reduces the cost of spectral transformations by up to 40%, enhancing the overall model efficiency by 15%-22%. Additionally, a series of tests confirmed the accuracy and stability of this new solver. This paper proposes a new non-hydrostatic spectral solver by applying a finite-volume method (FVM) into the spectral framework, where a horizontal divergence (D)- based structure equation is constructed and most of the prognostic variables as well as their horizontal gradients are calculated in grid point space directly. The number of spectral transforms is dramatically reduced. In practice, the cost of spectral transform with the proposed solver is reduced up to 40%. image

关键词： finite-volume method idealized tropical cyclone non-hydrostatic spectral model spectral transform

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On convergence of a fitted finite-volume method for the valuation of options on assets with stochastic volatilities

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IMA JOURNAL OF NUMERICAL ANALYSIS 2010年第4期30卷 1101-1120页

作者： Huang, C. -S. Hung, C. -H. Wang, Song Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 804 Taiwan Univ Western Australia Dept Math & Stat Crawley WA 6009 Australia

In this paper we present a convergence analysis for a fitted finite-volume discretization method for the two-dimensional Black-Scholes equation arising in the Hull-White model for pricing European options with stochastic volatility. We first formulate the finite-volume method as a nonconforming Petrov-Galerkin finite-element method with each basis function of the trial space being determined by a set of two-point boundary-value problems defined on element edges. We then show that the bilinear form of the finite-element method is coercive and continuous. Finally we establish an upper bound of order O(h) on the discretization error of method, where h denotes the mesh parameter of the discretization.

关键词： stochastic volatility European option pricing finite-volume method stability and convergence

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Observation of vector solitary waves in soft laminates using a finite-volume method

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INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 2020年 124卷 103502-103502页

作者： Ziv, Ron Shmuel, Gal Technion Israel Inst Technol Fac Mech Engn IL-32000 Haifa Israel

Soft materials with engineered microstructure support nonlinear waves which can be harnessed for various applications, from signal communication to impact mitigation. Such waves are governed by nonlinear coupled differential equations whose analytical solution is seldom trackable, hence emerges the need for suitable numerical solvers. Based on a finite-volume method in one space dimension, we here develop a designated scheme for nonlinear waves with two coupled components that propagate in soft laminates. We apply our scheme to a periodic laminate made of two alternating compressible Gent layers, and consider two cases. In one case, we analyze a motion whose component along the lamination direction is coupled to a component in the layers plane, and discover vector solitary waves in a continuum medium. In the second case, we analyze a motion with two coupled components in the plane of the layers, and observe a train of linearly polarized solitary waves, followed by a single circularly polarized wave. The framework we developed offers a platform for further investigation of these waves and their extension to higher dimensional problems.

关键词： finite-volume method Composites Laminates Soft materials Nonlinear elasticity finite deformations Wave propagation Solitary waves Shocks Gent material

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A Phase-Field-Based Hybrid Lattice-Boltzmann finite-volume method and Its Application to Simulate Droplet Motion under Electrowetting Control

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JOURNAL OF ADHESION SCIENCE AND TECHNOLOGY 2012年第12-17期26卷 1825-1851页

作者： Huang, J. J. Shu, C. Feng, J. J. Chew, Y. T. Natl Univ Singapore Dept Mech Engn Singapore 119260 Singapore Natl Univ Singapore Temasek Labs Singapore 117411 Singapore Univ British Columbia Dept Chem & Biol Engn Vancouver BC V6T 1Z3 Canada Univ British Columbia Dept Math Vancouver BC V6T 1Z2 Canada

A phase-field-based numerical model combining the lattice-Boltzmann method (LBM) and the finite-volume method (FVM) is proposed and applied for the study of two-dimensional (2-D) droplet under electrowetting (EW) control by using alternating current (AC). The new model overcomes several limitations of the pure LBM in interface dynamics, while keeping the key advantages of LBM for hydrodynamics. The model formulation is presented and some numerical issues are discussed. Droplet motions under EW control are investigated by using this method, with the focus on the effects of key control parameters on the induced droplet oscillation. This study may provide useful guidelines for mixing enhancement within the droplet by EW control. (C) Koninklijke Brill NV, Leiden, 2011

关键词： Droplet oscillation electrowetting AC control phase-field model lattice-Boltzmann method finite-volume method

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Modified finite-volume method based on a cell vertex scheme for the solution of radiative transfer problems in complex 3D geometries

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JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2011年第17期112卷 2661-2675页

作者： Trovalet, Lionel Jeandel, Gerard Coelho, Pedro J. Asllanaj, Fatmir Nancy Univ Inst Natl Polytech Lorraine CNRS LEMTA F-54504 Vandoeuvre Les Nancy France Inst Super Tecn Dept Mech Engn P-1049001 Lisbon Portugal

A modified finite-volume method based on a cell vertex scheme was applied to solve radiative transfer problems within a participating medium of complex three-dimensional shaped domain. The computational spatial domain of interest was divided into four-node tetrahedron elements with unstructured meshes while the adopted formulation was combined with a closure relation based on an exponential scheme. The studied medium was assumed to be grey, non-scattering and was bounded by black surfaces. Our results were then compared with those found in other articles on the subject. The approach shows a very good level of performance for wall heat transfer evaluation. Accurate results were obtained on coarse computational meshes and solution errors were found to decrease with grid refinement. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Radiative transfer finite-volume method Cell vertex scheme Complex 3D geometries Unstructured tetrahedral meshes

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A finite-volume method for deformation analysis of woven fabrics

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 1999年第12期46卷 2061-2098页

作者： Teng, JG Chen, SF Hu, JL Hong Kong Polytech Univ Dept Civil & Struct Engn Hong Kong Peoples R China Hong Kong Polytech Univ Inst Text & Clothing Hong Kong Peoples R China

Efficient numerical methods for simulating cloth deformations have been identified as the key to the development of successful Computer-Aided Design systems for clothing products. This paper presents the formulation of a new finite-volume method for the simulation of complex deformations of initially flat woven fabric sheets under self-weight or externally applied loading. The fabric sheet is assumed to undergo very large displacements and rotations but small strains during the process of deformation. The fabric material is assumed to be linear elastic and orthotropic. The fabric sheet is discretized into many small structured patches called finite volumes (or control volumes), each containing one grid node and several face nodes. The bending and membrane deformations of a typical volume can be defined using the global co-ordinates of its grid node and surrounding face nodes. The equilibrium equations governing the complex deformations are derived employing the principle of stationary total potential energy. These equations are solved using a single-step full Newton-Raphson method which is found to be capable of predicting the final deformed shape, the only result of interest in a fabric drape analysis. To speed up convergence, the line search technique is adopted with good effect. This single-step approach is more efficient than the step-by-step incremental approach employed in conventional non-linear finite element analysis of load-bearing structures. A number of example simulations of fabric drape/buckling deformations are included in the paper, which demonstrate the efficiency and validity of the proposed method. (C) 1999 John Wiley & Sons, Ltd.

关键词： finite-volume method fabric drape fabric deformations non-linear analysis fabric buckling numerical simulation

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Numerical simulations of non-isothermal three-dimensional flows in an extruder by a finite-volume method

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JOURNAL OF NON-NEWTONIAN FLUID MECHANICS 2005年第1期126卷 7-22页

作者： Khalifeh, A Clermont, JR Univ Grenoble 1 Inst Natl Polytech Grenoble CNRS UMR 5520Lab Rheol F-38041 Grenoble France

This study considers numerical applications of a finite-volume method to steady non-isothermal flows in geometries close to a single-screw extruder. Two geometrical configurations of the channel, with gap and zero gap, are investigated. The simulations concern incompressible fluids obeying different constitutive equations: Newtonian, generalized Newtonian with shear-thinning properties (Carreau-Yasuda law), and two viscoelastic differential models, the upper convected maxwell (UCM) and the Phan-Thien/Tanner (PTT). The temperature dependence is described by a Williams-Landel-Ferry (WLF) equation. For discretizing the equations and unknowns, we use a staggered grid with a QUICK scheme for the convective-type terms and solve the set of governing equations by a decoupled algorithm, stabilized by a pseudo- transient stress term and an elastic viscous stress splitting (EVSS) technique, in the viscoelastic case for the UCM model. The numerical results enable us to state the influence of temperature and rheological properties on the flow characteristics in the geometries investigated and underline the complex behaviour of the materials in such configurations. (c) 2005 Elsevier B.V. All rights reserved.

关键词： non-isothermal flows single-screw extruder finite-volume method viscoelasticity UCM and PTT fluids

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A primitive variable finite-volume method for incompressible viscous magnetohydrodynamic flows

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INTERNATIONAL JOURNAL OF COMPUTER APPLICATIONS IN TECHNOLOGY 1998年第3-5期11卷 170-176页

作者： Agarwal, RK Wichita State Univ Wichita KS 67260 USA

A recently developed numerical method is employed for computing the numerical solutions of the incompressible Navier-Stokes equations in the presence of a magnetic field. The method is based on the pressure correction approach, but employs a regular grid finite-volume variable arrangement instead of the usual staggered grid arrangement. The pressure equation is derived such that effects which promote the well-known checkerboard instability are not present. A relevant compatibility constraint on pressure is satisfied by Neumann boundary conditions obtained using a vector identity. The transport equations of the magnetic field with solenoidal condition are solved with a similar approach. The unified computational framework is thus developed for the solution of incompressible viscous magnetohydrodynamic flows. Implemented in a second-order-accurate finite-volume code, the algorithm is used to compute the magnetohydrodynamic flow in a pipe. Numerical solution is compared with existing analytical and computational results for various Hartmann numbers.

关键词： finite-volume method incompressible flows viscous magnetohydrodynamic flows

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A finite-volume method for contact drape simulation of woven fabrics and garments

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finite ELEMENTS IN ANALYSIS AND DESIGN 2001年第6-7期37卷 513-531页

作者： Chen, SF Hu, JL Teng, JG Hong Kong Polytech Univ Dept Civil & Struct Engn Kowloon Hong Kong Peoples R China Hong Kong Polytech Univ Inst Text & Clothing Kowloon Hong Kong Peoples R China

Draping of woven fabrics and garments interacting with rigid objects or human bodies is a large displacement/rotation contact problem of anisotropic materials. The objective of this paper is to extend a geometrically nonlinear finite-volume method recently developed by the authors to predict contact drape deformations of woven fabrics. In this finite volume method, an initially flat woven fabric sheet is first divided into a number of structured finite volumes (or control volumes) using mesh lines along the warp and weft directions. The out-of-plane bending and in-plane membrane strain energies of the fabric sheet are then found by summing up the contributions from all control volumes. The equilibrium equations of the fabric sheet are derived employing the principle of stationary total potential energy and solved using the full Newton-Raphson method with line searches. In this paper, a simple and easily achievable algorithm for detecting and treating fabric contact with a rigid object is proposed and shown to be effective and efficient. Numerical simulation of two square fabric sheets draped over a round rod is first considered. The coordinates of a characteristic point of the first fabric sheet after drape deformation predicted using the present method are compared with available experimental results, showing a close match between the two approaches. Numerical results of square fabric sheets draped over a sphere and skirts attached to and draped over a synthetic body form are next presented. The predicted drape shapes are realistic. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： fabric drape fabric deformation contact problem finite-volume method numerical simulation nonlinear analysis Newton-Raphson method

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Development of a parallel semi-implicit two-dimensional plasma fluid modeling code using finite-volume method

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COMPUTER PHYSICS COMMUNICATIONS 2012年第6期183卷 1225-1236页

作者： Lin, K-M. Hung, C-T. Hwang, F-N. Smith, M. R. Yang, Y-W. Wu, J-S. Natl Chiao Tung Univ Dept Mech Engn Hsinchu Taiwan Natl Cent Univ Dept Math Tao Yuan Taiwan Natl Ctr High Performance Comp Hsinchu Taiwan

In this paper, the development of a two-dimensional plasma fluid modeling code using the cell-centered finite-volume method and its parallel implementation on distributed memory machines is reported. Simulated discharge currents agree very well with the measured data in a planar dielectric barrier discharge (DBD). Parallel performance of simulating helium DBD solved by the different degrees of overlapping of additive Schwarz method (ASM) preconditioned generalized minimal residual method (GMRES) for different modeling equations is investigated for a small and a large test problem, respectively, employing up to 128 processors. For the large test problem, almost linear speedup can be obtained by using up to 128 processors. Finally, a large-scale realistic two-dimensional DBD problem is employed to demonstrate the capability of the developed fluid modeling code for simulating the low-temperature plasma with complex chemical reactions. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Additive Schwarz method (ASM) finite-volume method Local mean energy approximation (LMEA) Parallel computing Plasma fluid modeling

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