Chun Yang¹, Dalin Tang², Chun Yuan³, William Kerwin², Fei Liu³, Gador Canton³, Thomas S. Hatsukami^3,4, Satya Atluri⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.2, pp. 95-108, 2008, DOI:10.3970/cmes.2008.028.095

Abstract Atherosclerotic plaque rupture and progression have been the focus of intensive investigations in recent years. Plaque rupture is closely related to most severe cardiovascular syndromes such as heart attack and stroke. A computational procedure based on meshless generalized finite difference (MGFD) method and serial magnetic resonance imaging (MRI) data was introduced to quantify patient-specific carotid atherosclerotic plaque growth functions and simulate plaque progression. Participating patients were scanned three times (T₁,T₂, and T₃, at intervals of about 18 months) to obtain plaque progression data. Vessel wall thickness (WT) changes were used as the measure for plaque progression. Since there was insufficient… More >

S.P. Hu¹, D.L. Young², C.M. Fan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.1, pp. 1-20, 2008, DOI:10.3970/cmes.2008.024.001

Abstract In this paper, a novel numerical scheme called (FDMFS), which combines the finite difference method (FDM) and the method of fundamental solutions (MFS), is proposed to simulate the nonhomogeneous diffusion problem with an unsteady forcing function. Most meshless methods are confined to the investigations of nonhomogeneous diffusion equations with steady forcing functions due to the difficulty to find an unsteady particular solution. Therefore, we proposed a FDM with Cartesian grid to handle the unsteady nonhomogeneous term of the equations. The numerical solution in FDMFS is decomposed into a particular solution and a homogeneous solution. The particular solution is constructed using… More >

A. J. Davies¹, D. Crann¹, S. J. Kane¹, C-H. Lai²

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.2, pp. 79-86, 2007, DOI:10.3970/cmes.2007.018.079

Abstract The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The… More >

Sacia Kachi^1,*, Fatima-zohra Bensouici¹, Nawel Ferroudj¹, Saadoun Boudebous²

FDMP-Fluid Dynamics & Materials Processing, Vol.15, No.2, pp. 89-105, 2019, DOI:10.32604/fdmp.2019.00263

Abstract The objective of the present study is to analyze the laminar mixed convection in a square cavity with moving cooled vertical sidewalls. A constant flux heat source with relative length l is placed in the center of the lower wall while all the other horizontal sides of the cavity are considered adiabatic. The numerical method is based on a finite difference technique where the spatial partial derivatives appearing in the governing equations are discretized using a high order scheme, and time advance is dealt with by a fourth order Runge Kutta method. The Richardson number (Ri), which represents the relative… More >

Anupam Bh,ari¹, Vipin Kumar²

FDMP-Fluid Dynamics & Materials Processing, Vol.10, No.3, pp. 359-375, 2014, DOI:10.3970/fdmp.2014.010.359

Abstract The purpose of this paper is to study the flow characteristics of a ferrofluid revolving through a porous medium with a magnetic-field-dependent viscosity in the presence of a stationary disk. A Finite Difference Method is employed to discretize the set of nonlinear coupled differential equations involved in the problem. The discretized nonlinear equations, in turn, are solved by a Newton method (using MATLAB) taking the initial guess with the help of a PDE Solver. Results displayed in graphical form are used to assess the effect of the variable viscosity and porosity parameters on the velocity components. The displacement thickness of… More >

Paras Ram^1,2, Vikas Kumar³

FDMP-Fluid Dynamics & Materials Processing, Vol.10, No.2, pp. 179-196, 2014, DOI:10.3970/fdmp.2014.010.179

Abstract The present study is carried out to examine the effects of temperature dependent variable viscosity on the three dimensional steady axi-symmetric Ferrohydrodynamic (FHD) boundary layer flow of an incompressible electrically nonconducting magnetic fluid in the presence of a rotating disk. The disk is subjected to an externally applied magnetic field and is maintained at a uniform temperature. The nonlinear coupled partial differential equations governing the boundary layer flow are non dimensionalized using similarity transformations and are reduced to a system of coupled ordinary differential equations. To study the effects of temperature dependent viscosity on velocity profiles and temperature distribution within… More >

Chia-Ming Fan^1,2, Chein-Shan Liu³, Weichung Yeih¹, Hsin-Fang Chan¹

CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 67-86, 2010, DOI:10.3970/cmc.2010.015.067

Abstract In this study, the nonlinear obstacle problems, which are also known as the nonlinear free boundary problems, are analyzed by the scalar homotopy method (SHM) and the finite difference method. The one- and two-dimensional nonlinear obstacle problems, formulated as the nonlinear complementarity problems (NCPs), are discretized by the finite difference method and form a system of nonlinear algebraic equations (NAEs) with the aid of Fischer-Burmeister NCP-function. Additionally, the system of NAEs is solved by the SHM, which is globally convergent and can get rid of calculating the inverse of Jacobian matrix. In SHM, by introducing a scalar homotopy function and… More >