G. C. Bourantas¹, E. D. Skouras^2,3, V. C. Loukopoulos⁴, G. C. Nikiforidis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.2, pp. 187-212, 2010, DOI:10.3970/cmes.2010.064.187

Abstract Meshfree point collocation method (MPCM) is developed, solving the velocity-vorticity formulation of Navier-Stokes equations, for two-dimensional, steady state incompressible viscous flow problems in the presence of heat transfer. Particular emphasis is placed on the application of the velocity-correction method, ensuring the continuity equation. The Gaussian Radial Basis Functions (GRBF) interpolation is employed to construct the shape functions in conjunction with the framework of the point collocation method. The cases of forced, natural and mixed convection in a 2D rectangular enclosure are examined. The accuracy and the stability of the proposed scheme are demonstrated through three More >

A.I.Tolstykh, D.A. Shirobokov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 207-222, 2005, DOI:10.3970/cmes.2005.007.207

Abstract A way of using RBF as the basis for PDE's solvers is presented, its essence being constructing approximate formulas for derivatives discretizations based on RBF interpolants with local supports similar to stencils in finite difference methods. Numerical results for different types of elasticity equations showing reasonable accuracy and good$h$-convergence properties of the technique are presented. Applications of the technique to problems with non-self-adjoint operators (like those for the Navier-Stokes equations) are also considered. More >

C. Shu^1,2, H. Ding², K.S. Yeo²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 195-206, 2005, DOI:10.3970/cmes.2005.007.195

Abstract Local radial basis function-based differential quadrature (RBF-DQ) method was recently proposed by us. The method is a natural mesh-free approach. It can be regarded as a combination of the conventional differential quadrature (DQ) method with the radial basis functions (RBFs) by means of taking the RBFs as the trial functions in the DQ scheme. With the computed weighting coefficients, the method works in a very similar fashion as conventional finite difference schemes. In this paper, we mainly concentrate on the applications of the method to incompressible flows in the steady and unsteady regions. The multiquadric More >

Tong-qing Guo, Zhi-liang Lu¹

CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 105-112, 2005, DOI:10.3970/cmc.2005.002.105

Abstract In this paper, a rapid deforming technique is developed to generate dynamic, three-dimensional, multi-block, mesh. The second-order Runge-Kutta time-marching method is used to solve the structural equations of motion. A dual-time method and finite volume discretization are applied for the unsteady Euler/Navier-Stokes equations to calculate the aerodynamic forces, in which the physical time step is synchronous with the structural equations of motion. The Spalart-Allmaras turbulence model is adopted for a turbulent flow. Due to mass dissimilarity, exiting in flutter calculations for a compressible flow, methods of variable mass and variable stiffness are developed to calculate More >

C.T. Lee¹, C.C. Lee²

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.5, pp. 375-403, 2015, DOI:10.3970/cmes.2015.104.375

Abstract In this article, we demonstrate a numerical 3-D chip, and studied the capillary dynamics inside the microchannel. We applied the level set method on the Navier-Stokes equation which incorporates the surface tension and two-phase flow characteristics. We analyzed the capillary dynamics near the junction of two microchannels. Such a highlighting point is important that it not only can provide the information of interface behavior when fluids are made into a head-on collision, but also emphasize the idea for the design of the chip. In addition, we study the pressure distribution of the fluids at the More >

Jason F. Hammond¹, Elizabeth J. Stewart², John G. Younger³, Michael J.Solomon², David M. Bortz^4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.3, pp. 295-340, 2014, DOI:10.32604/cmes.2014.098.295

Abstract The overall goal of this work is to develop a numerical simulation which correctly describes a bacterial biofilm fluid-structure interaction and separation process. In this, the first of a two-part effort, we fully develop a convergent scheme and provide numerical evidence for the method order as well as a full 3D separation simulation. We use an immersed boundary-based method (IBM) to model and simulate a biofilm with density and viscosity values different from than that of the surrounding fluid. The simulation also includes breakable springs connecting the bacteria in the biofilm which allows the inclusion… More >

Zhendong Luo¹, Fei Teng²

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.1, pp. 33-58, 2014, DOI:10.3970/cmes.2014.101.033

Abstract A semi-discrete Crank-Nicolson (CN) formulation about time and a fully discrete stabilized CN finite volume element (SCNFVE) formulation based on two local Gauss integrals and parameter-free with the second-order time accuracy are established for the non-stationary Navier-Stokes equations. The error estimates of the semi-discrete and fully discrete SCNFVE solutions are derived. Some numerical experiments are presented to illustrate that the fully discrete SCNFVE formulation possesses more advantages than its stabilized finite volume element formulation with the first-order time accuracy, thus validating that the fully discrete SCNFVE formulation is feasible and efficient for finding the numerical More >

B.-H. Lee¹, J.-C. Park², M.-H. Kim³, S.-C. Hwang²

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.2, pp. 89-112, 2011, DOI:10.3970/cmes.2011.075.089

Abstract The violent free-surface motions and the corresponding impact loads are numerically simulated by using the refined Moving Particle Simulation (MPS) method, which was originally proposed by Koshizuka and Oka (1996) for incompressible flows. In the present method, accuracy and efficiency are significantly improved compared to the original MPS method by using optimal source term, optimal gradient and collision models, and improved solid-boundary treatment and search of free-surface particles. The refined MPS method was verified through comparisons against Kishev et al.'s (2006) sloshing experiment. It is also demonstrated that the refined MPS method is excellent in More >

Dongjie Liu¹, Dehao Yu²

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 305-330, 2008, DOI:10.3970/cmes.2008.037.305

Abstract The coupling method of natural boundary element and mixed finite element is applied to analyze the stationary Navier-Stokes equation in 2-D unbounded domains. After an artificial smooth boundary is introduced, the original nonlinear problem is reduced into an equivalent problem defined in bounded computational domain. The well-posedness of the reduced problem is proved. The finite element approximation of this problem is given, and numerical example is provided to show the feasibility and efficiency of the method. More >

Marcin Kamiński¹, Rafał Leszek Ossowski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 311-334, 2011, DOI:10.3970/cmes.2011.081.311

Abstract The main aim of this article is numerical solution of the fully coupled Navier-Stokes equations with Gaussian random parameters. It is provided thanks to the specially adopted Finite Volume Method, modified using the generalized stochastic perturbation technique. This Stochastic Finite Volume Method is applied to model 3D problem with uncertainty in liquid viscosity and a coefficient of the heat conduction, separately. Probabilistic moments and characteristics of up to the fourth order are determined with the use of the Response Function Method realized numerically via the polynomial inpterpolation. Although mathematical formulation of the SFVM has been More >