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Van Veldhuizen, S. (author), Vuik, C. (author), Kleijn, C.R. (author)In this study various numerical schemes for simulating 2D laminar reacting gas flows, as typically found in Chemical Vapor Deposition (CVD) reactors, are proposed and compared. These systems are generally modeled by means of many stiffly coupled elementary gas phase reactions between a large number of reactants and intermediate species. The...report 2006
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Tang, J.M. (author), Vuik, C. (author)For various applications, it is well-known that deflated ICCG is an efficient method for solving linear systems with invertible and singular co-efficient matrix. This deflated ICCG with subdomain deflation vectors is used by us to solve linear systems with singular coefficient matrix, arising from a discretization of the Poisson equation with...report 2006
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- Brusche, J.H. (author), Segal, A. (author), Vuik, C. (author) report 2006
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- Tang, J.M., (author), Vuik, C. (author) report 2005
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Tang, J.M., (author), Vuik, C. (author)In this report we give new insights into the properties of invertible and singular deflated and preconditioned linear systems where the coefficient matrices are also symmetric and positive (semi-) definite. First we prove that the invertible de ated matrix has always a more favorable effeective condition number compared to the original matrix....report 2005
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Javierre, E. (author), Vuik, C. (author), Vermolen, F.J. (author), Segal, A. (author)A mathematical model is proposed for the dissolution of stoichiometric particles in binary alloys occurring during the heat treatments of as-cast aluminium alloys prior to hot extrusion. The Level Set method is used to capture the interface location implicitly. The front velocity, only dened on the moving interface, should be advected to the...report 2005
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Javierre, E. (author), Vuik, C. (author), Vermolen, F.J. (author), van der Zwaag, S. (author)In this paper we present a critical comparison of the suitability of several numerical methods, level set, moving grid and phase eld model, to address two well known Stefan problems in phase transformation studies: melting of a pure phase and diusional solid state phase transformations in a binary system. Similarity solutions are applied to...report 2005
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Nabben, R. (author), Vuik, C. (author)In this paper we compare various preconditioners for the numerical solution of partial differential equations. We compare the well-known balancing Neumann Neumann preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the deflated preconditioned system is...report 2004
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Erlangga, Y.A. (author), Oosterlee, C.W. (author), Vuik, C. (author)An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the...report 2004
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Li, C. (author), Vuik, C. (author)In this paper, some theoretical results on the eigenvalue analysis of the SIMPLER preconditioning for incompressible now is presented. Some formulations have been derived to characterize the spectrum of the preconditioned matrix. These results could be helpful for the practical use of the SIMPLER preconditioning. Some numerical tests are reported.report 2003
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Nabben, R. (author), Vuik, C. (author)In this paper we compare various preconditioners for the numerical solution of partial dierential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the de ated preconditioned system is always, i.e. for all...report 2003
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- Vuik, C. (author), Erlangga, Y.A., Oosterlee, C.W. (author) report 2003
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Van der Pijl, S.P. (author), Segal, A. (author), Vuik, C. (author)The Mass-Conserving Level-Set (MCLS) method is proposed to model multi-phase flows. The aim is to model high density-ratio flows with complex interface topologies, such as mixtures of bubbles and droplets. Aspects which are taken into account are: a sharp front (density changes rapidly), arbitrary shaped interfaces, surface tension, buoyancy and...report 2003
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- Erlangga, Y.A. (author), Vuik, C. (author), Oosterlee, C.W. (author) report 2003
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Vermolen, F.J. (author), Vuik, C. (author)A general model for the dissolution of particles in multi-component alloys is proposed and analyzed. The model is based on diffusion equations with cross-terms for the several species, combined with a Stefan condition as the equation of motion of the interface between the particle and diffusant phase. To facilitate the analysis we use a...report 2003
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Vermolen, F.J. (author), Vuik, C. (author), Van der Zwaag, S. (author)This paper is a review of a suite of mathematical models of increasing complexity on particle dissolution in metallic alloys. This work deals with models for multi-component particle dissolution in multi-component alloys, where various chemical species diffuse simultaneously, and a two-dimensional model incorporating interfacial reactions as in...report 2002
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Li, C. (author), Vuik, C. (author)In this paper, an eigenvalue analysis of the SIMPLE preconditioning for incompressible flow is presented. Some formulations have been set up to characterize the spectrum of the preconditioned matrix. This leads to a generalized eigenvalue problem. The generalized eigenvalue problem is investigated. Some eigenvalue bounds and the estimation for...report 2002
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Vermolen, F.J. (author), Vuik, C. (author), Segal, A. (author)We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous coefficients that vary in several orders of...report 2002
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Vuik, C. (author), Saghir, A. (author)Numerical modeling of the melting and combustion process is an important tool in gaining understanding of the physical and chemical phenomena which occur in a gas- or oil-fired glass melting furnace. The incompressible Navier-Stokes equations are used to model the gas now in the furnace. The discrete Navier-Stokes equations are solved by the...report 2002
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- Vuik, C. (author), Segal, A. (author), el Yaakoubi, L. (author), Dufour, E. (author) report 2001