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 >

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… 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 More >

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 >

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 More >

Roland Martin¹, Carlos Couder-Castaneda¹

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.1, pp. 47-78, 2010, DOI:10.3970/cmes.2010.063.047

Abstract We develop an unsplit convolutional perfectly matched layer (CPML) technique to absorb efficiently compressible viscous flows and their related supersonic or subsonic regimes at the outer boundary of a distorted computational domain. More particularly subsonic outgoing flows or subsonic wall-boundary layers close to the PML are well absorbed, which is difficult to obtain without creating numerical instabilities over long time periods. This new PML (CPML) introduces the calculation of auxiliary memory variables at each time step and allows an unsplit formulation of the PML. Damping functions involving a high shift in the frequency domain allow… More >

F.P. Mariano¹, L.Q. Moreira¹, A. Silveira-Neto¹, C.B. da Silva², J.C.F. Pereira²

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 181-216, 2010, DOI:10.3970/cmes.2010.059.181

Abstract A new numerical methodology combining Fourier pseudo-spectral and immersed boundary methods - IMERSPEC - is developed for fluid flow problems governed by the incompressible Navier-Stokes equations. The numerical algorithm consists in a classical Fourier pseudo-spectral methodology using the collocation method where wall boundary conditions are modelled by using an immersed boundary method (IBM). The performance of that new methodology is exemplified in two-dimensional numerical simulations of Green-Taylor decaying vortex, lid-driven cavity and flow over a square cylinder. The convergence rate, the accuracy, the influence of the Reynolds number and the external domain size are analyzed. More >

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

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 31-64, 2010, DOI:10.3970/cmes.2010.059.031

Abstract A meshfree point collocation method has been developed for the velocity-vorticity formulation of two-dimensional, steady state incompressible Navier-Stokes equations. Particular emphasis was placed on the application of the velocity-correc -tion method, ensuring the continuity equation. The Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are obtained for regular and irregular nodal distributions, stressing the positivity conditions that make the matrix of the system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated More >

S. Aland¹, J. Lowengrub², A. Voigt¹

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.1, pp. 77-108, 2010, DOI:10.3970/cmes.2010.057.077

Abstract We present a new method for simulating two-phase flows in complex geometries, taking into account contact lines separating immiscible incompressible components. We combine the diffuse domain method for solving PDEs in complex geometries with the diffuse-interface (phase-field) method for simulating multiphase flows. In this approach, the complex geometry is described implicitly by introducing a new phase-field variable, which is a smooth approximation of the characteristic function of the complex domain. The fluid and component concentration equations are reformulated and solved in larger regular domain with the boundary conditions being implicitly modeled using source terms. The… 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 >