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 solutions of the non-stationary Navier-Stokes… More >

K.Y. Volokh^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 87-101, 2013, DOI:10.3970/cmes.2013.092.087

Abstract In the laminar mode interactions among molecules generate friction between layers of water that slide with respect to each other. This friction triggers the shear stress, which is traditionally presumed to be linearly proportional to the velocity gradient. The proportionality coefficient characterizes the viscosity of water. Remarkably, the standard Navier-Stokes model surmises that materials never fail – the transition to turbulence can only be triggered by some kinematic instability of the flow. This premise is probably the reason why the Navier-Stokes theory fails to explain the so-called subcritical transition to turbulence with the help of the linear instability analysis. When… More >

V. C. Loukopoulos¹, G. C. Bourantas²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 531-558, 2012, DOI:10.3970/cmes.2012.088.531

Abstract Meshless Local Petrov-Galerkin (MLPG) approach is used for the solution of the Navier-Stokes and energy equations. More specific as a special case we apply the MLPG6 approach. In the MLPG6 method, the test function is chosen to be the same as the trial function (Galerkin method). The MLPG local weak form is written over a local sub-domain which is completely independent from the trial or test functions. The sizes of nodal trial and test function domains, as well as the size of the local sub-domain over which the local weak-form is considered, can be arbitrary. This may lead to either… 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 mass conservation regardless of length… 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 >

S. Chantasiriwan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 137-146, 2006, DOI:10.3970/cmes.2006.015.137

Abstract The multiquadric collocation method is the collocation method based on radial basis function known as multiquadrics. It has been successfully used to solve several linear and nonlinear problems. Although fluid flow problems are among problems previously solved by this method, there is still an outstanding issue regarding the influence of the free parameter of multiquadrics (or the shape parameter) on the performance of the method. This paper provides additional results of using the multiquadric collocation method to solve the lid-driven cavity flow problem. The method is used to solve the problem in the stream function-vorticity formulation and the velocity-vorticity formulation.… 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 proposed in addition to the… More >

K.S. Kim¹, B.H. Lee², M.H. Kim¹, J.C. Park³

CMES-Computer Modeling in Engineering & Sciences, Vol.79, No.3&4, pp. 201-222, 2011, DOI:10.3970/cmes.2011.079.201

Abstract The coupling and interactions between vessel motion and inner-tank sloshing are investigated by a potential-CFD (Computational Fluid Dynamics) hybrid method in time domain. Potential-theory-based 3D diffraction/radiation panel program is used to obtain the hydrodynamic coefficients and wave forces for the simulation of vessel motion in time domain. The liquid sloshing in tanks is simulated in time domain by using the improved Moving Particle Simulation (PNU-MPS) method and it is validated through comparison against sloshing experiments. The calculated sloshing tank forces and moments are applied to the vessel-motion simulation as excitation forces and moments. The updated ship motion, which is influenced… More >

J. Badur¹, M. Karcz¹, M. Lemanski¹, L. Nastalek¹

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.3, pp. 299-310, 2011, DOI:10.3970/cmes.2011.073.299

Abstract In the paper we propose to remove the classical Navier slip condition and replace it with new generalized Navier-Stokes slip boundary conditions. These conditions are postulated to be ones following from the mass and momentum balance within a thin, shell-like moving boundary layer. Owing to this, the problem consistency between the internal and external friction in a viscous fluid is solved within the framework of a proper form of the layer balances, and a proper form of constitutive relations for appropriate friction forces. Finally, the common features of the Navier, Stokes, Maxwell and Reynolds concepts of a boundary slip layer… More >

Zhiming Gao², Yichen Ma³

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 135-164, 2010, DOI:10.3970/cmes.2010.066.135

Abstract Shape optimization technique has an increasing role in fluid dynamics problems governed by distributed parameter systems. In this paper, we present the problem of shape optimization of two dimensional viscous flow governed by the time dependent Navier-Stokes equations. The minimization problem of the viscous dissipated energy was established in the fluid domain. We derive the structure of continuous shape gradient of the cost functional by using the differentiability of a saddle point formulation with a function space parametrization technique. Finally a gradient type algorithm with mesh adaptation and mesh movement strategies is successfully and efficiently applied. More >