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Time Levels (time + level)
Selected AbstractsApproximation of time-dependent, viscoelastic fluid flow: Crank-Nicolson, finite element approximation,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2004Vincent J. Ervin Abstract In this article we analyze a fully discrete approximation to the time dependent viscoelasticity equations with an Oldroyd B constitutive equation in ,, = 2, 3. We use a Crank-Nicolson discretization for the time derivatives. At each time level a linear system of equations is solved. To resolve the nonlinearities we use a three-step extrapolation for the prediction of the velocity and stress at the new time level. The approximation is stabilized by using a discontinuous Galerkin approximation for the constitutive equation. For the mesh parameter, h, and the temporal step size, ,t, sufficiently small and satisfying ,t , Ch, existence of the approximate solution is proven. A priori error estimates for the approximation in terms of ,t and h are also derived. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 248,283, 2004 [source] Linear stability analysis and fourth-order approximations at first time level for the two space dimensional mildly quasi-linear hyperbolic equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2001R. K. Mohanty Abstract In 1996, Mohanty et al. [1] presented a fourth-order finite difference solution of a two space dimensional nonlinear hyperbolic equation with Dirichlet boundary conditions. In 1998, Mohanty et al. [2] discussed a fourth-order approximation at first time level for the numerical solution of the one space dimensional hyperbolic equation. In both the cases, they have discussed the stability analysis for the linear hyperbolic equation having first-order space derivative terms. Recently, Mohanty et al. [3] have developed fourth-order difference formulas for the three space dimensional quasi-linear hyperbolic equations and obtained fourth-order approximation at first time level. In this article, we extend our strategy for solving the two space dimensional quasi-linear hyperbolic equation. An operator splitting method for a linear hyperbolic equation having a time derivative term is proposed. Linear stability analysis and fourth-order approximation at first time level for the two space dimensional quasi-linear hyperbolic equation are also discussed. The results of the numerical experiments are compared with the exact solution. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 607,618, 2001 [source] A visual incompressible magneto-hydrodynamics solver with radiation, mass, and heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2009Necdet AslanArticle first published online: 8 JAN 200 Abstract A visual two-dimensional (2D) nonlinear magneto-hydrodynamics (MHD) code that is able to solve steady state or transient charged or neutral convection problems under the radiation, mass, and heat transfer effects is presented. The flows considered are incompressible and the divergence conditions on the velocity and magnetic fields are handled by similar relaxation schemes in the form of pseudo-iterations between the real time levels. The numerical method utilizes a matrix distribution scheme that runs on structured or unstructured triangular meshes. The time-dependent algorithm developed here utilizes a semi-implicit dual time stepping technique with multistage Runge-Kutta (RK) algorithm. It is possible for the user to choose different normalizations (natural, forced, Boussinesq, Prandtl, double-diffusive and radiation convection) automatically. The code is visual and runs interactively with the user. The graphics algorithms work multithreaded and allow the user to follow certain flow features (color graphs, vector graphs, one-dimensional profiles) during runs, see (Comput. Fluids 2007; 36:961,973) for details. With the code presented here nonlinear steady or time-dependent evolution of heated and stratified neutral and charged liquids, convection of mixture of neutral and charged gases, double-diffusive and salinity natural convection flows with internal heat generation/absorption and radiative heat transfer flows can be investigated. In addition, the numerical method (combining concentration, radiation, heat transfer, and MHD effects) takes the advantage of local time stepping and employs simplified residual jacobian matrix to increase pseudo-convergence rate. This code is currently being improved to simulate three-dimensional problems with parallel processing. Copyright © 2009 John Wiley & Sons, Ltd. [source] Anisotropic mesh adaption for time-dependent problems,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2008S. Micheletti Abstract We propose a space,time adaptive procedure for a model parabolic problem based on a theoretically sound anisotropic a posteriori error analysis. A space,time finite element scheme (continuous in space but discontinuous in time) is employed to discretize this problem, thus allowing for non-matching meshes at different time levels. Copyright © 2008 John Wiley & Sons, Ltd. [source] Clinical characteristics of children with snakebite poisioning and management of complications in the pediatric intensive care unitPEDIATRICS INTERNATIONAL, Issue 6 2005Gonca Ozay AbstractBackground:,Venomous snakebite is an emergency condition with high morbidity and mortality in childhood. Nearly all venomous snakes in Turkey are members of the Viperidae family and show poisonous local and hematotoxic effects. Methods:,A total of 77 children (mean age 9.9 ± 2.9 years; age range 3,14 years) with venomous snakebites were investigated. General characteristics of the children, species of the snakes, localization of the bite, clinical and laboratory findings, treatment approaches, complications and prognosis were evaluated. Results:,The male to female ratio was 1.4. Ninety-one per cent of cases were from rural areas. Most of the bites were seen in May and June. Mean duration between snakebites and admissions to our department was 13 ± 6.5 h. According to a clinical grading score, 57.1% of patients presented to us as grade II. Mean leukocyte count, aspartate aminotransferase, lactate dehydrogenase, creatinine phosphokinase and protrombin time levels were above the normal ranges and mean activated partial tromboplastin time was below the normal range. Platelet counts inversely correlated with the grading score and duration of hospitalization. The most common complication that occurred during the treatment was tissue necrosis (13%). The mean hospital stay time was 6.3 ± 6 days. Three children with disseminated intravascular coagulation died. Fasciotomies were performed to seven (9.1%) children due to compartment syndrome. Of 10 children with tissue necrosis, three (3.9%) had finger amputation and seven (9.1%) had toe amputation. Higher grading score on admission, platelet count below 120 000/mm3, AST over 50 IU/L and existence of evident ecchymosis were found as significant risk factors for development of serious complications by logistic regression analysis. Conclusions:,Snakebite poisoning is an emergency medical condition that is particularly important in childhood. The envenomations are still considerable public health problems with a high morbidity and mortality in rural areas of Turkey. [source] In Vitro and Computational Thrombosis on Artificial Surfaces With Shear StressARTIFICIAL ORGANS, Issue 7 2010Scott C. Corbett Abstract Implantable devices in direct contact with flowing blood are associated with the risk of thromboembolic events. This study addresses the need to improve our understanding of the thrombosis mechanism and to identify areas on artificial surfaces susceptible to thrombus deposition. Thrombus deposits on artificial blood step transitions are quantified experimentally and compared with shear stress and shear rate distributions using computational fluid dynamics (CFD) models. Larger steps, and negative (expanding) steps result in larger thrombus deposits. Fitting CFD results to experimental deposit locations reveals a specific shear stress threshold of 0.41 Pa or a shear rate threshold of 54 s,1 using a shear thinning blood viscosity model. Thrombosis will occur below this threshold, which is specific to solvent-polished polycarbonate surfaces under in vitro coagulation conditions with activated clotting time levels of 200,220 s. The experimental and computational models are valuable tools for thrombosis prediction and assessment that may be used before proceeding to clinical trials and to better understand existing clinical problems with thrombosis. [source] | ||||||||||