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Showing 1 to 20 of 28 for “"Crank-Nicolson"”.
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Numerical Simulations of Viscoelastic Flows Using the Discontinuous Galerkin Method
… using the discontinuous Galerkin method. The Crank-Nicolson scheme is used for the temporal discretization of the Navier-Stokes equations in order to achieve a second-order accuracy in time, while the optimal third-order total-variation diminishing Runge-Kutta scheme is used for the temporal …
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Simulation of temperature history and estimation of thermal properties of food materials during freezing
… presented and used to assess the accuracy of the Crank-Nicolson and the Two-Step methods in solving this nonlinear problem. Overall, the accuracy of the Two-Step method was higher than that of the Crank-Nicolson method. These numerical methods were also implemented to simulate one-dimensional …
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A finite element analysis of high kappa, high field Ginzburg-Landau type model of superconductivity
… discretization in space and Backward-Euler and Crank-Nicolson discretization schemes in time. We establish existence and uniqueness results for the fully-discrete equations as well as optimal L2 and HI error estimates for the Backward-Euler-Galerkin and the Crank-Nicolson-Galerkin problems. …
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Finite element approximations for fluid flows governed by nonlinear slip boundary conditions of friction type: from theory to computations
… study of the stability for all positive time of Crank-Nicolson scheme for the two-dimensional Navier-Stokes equation driven by slip boundary conditions of “friction type”. We discretize these equations in time using the Crank-Nicolson scheme and in space using finite element approximation. We …
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Methodologies for Transient Simulation of Hybrid Electromagnetic/Circuit Systems with Multiple Time Scales
… portions. Additionally, the use of the Crank-Nicolson integration scheme is investigated for the simulation of transmission line structures, and an efficient methodology is proposed by combining the Crank-Nicolson integration of transmission lines and standard integration of circuits. …
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Digital Simulation of Compaction in Sedimentary Sequences
… to vary with temperature and pressure. The Crank-Nicolson finite difference method is used to solve the partial differential equations of fluid flow and energy transport. Distributions of excess pressure and temperature are analyzed for several cases: shales, alternating layers of shale and …
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Numerical Solutions to PDE Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs
… Burgard and Kjaer (2011). In particular, we use Crank-Nicolson finite-difference scheme to solve Black-Scholes risk-free PDE, for European and American options, and show how this numerical solution approach is extendable to solve the risky PDE for the value of the same derivative using the same …
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The application of high order finite difference methods to the diffusion-convection equation
… using five adjacent space node points by the Crank - Nicolson formulation. This method is referred to as the 5PFDM. It has fourth order correctness in space truncation error and shows good approximation to the solution of the equation in a normalized, dimensionless fluid system and also in a …
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SOLVING THE CABLE EQUATION, A SECOND-ORDER TIME DEPENDENT PDE FOR NON-IDEAL CABLES WITH ACTION POTENTIALS IN THE MAMMALIAN BRAIN USING KSS METHODS
… method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal …
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An analysis of the TR-BDF2 integration scheme
… due to insufficient numerical damping from the Crank-Nicolson method (which is based on the Trapezoidal rule) and demonstrate how these problems can be rectified with the TR-BDF2 scheme. Several examples are presented, including an advection-diffusion-reaction (ADR) problem and the (chaotic) …
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Implicit-explicit methods for time-dependent PDE’s
… schemes such as the popular combination of Crank-Nicolson with second order Adams-Bashforth is discouraged and better alternatives are proposed. Our findings are demonstrated on several examples.
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Computational analysis of viscoelastic fluid dynamics with applications to heat exchangers
… finite difference method integrated with the Crank-Nicolson scheme. The pressure-velocity coupling in the momentum equations is resolved by employing the Semi-Implicit Method for Pressure Linked Equations (SIMPLE). To cope with numerical diffusion and numerical stability issues the treatment …
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On the prediction of electronic stopping power from first principles
… are numerically integrated according to the Crank-Nicolson integrator algorithm. In this work a correction to the existing Crank-Nicolson algorithm was implemented in parallel, based on using the correct time-dependent Kohn-Sham equation involving the covariant derivative of the wavefunction …
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Entwicklung und Anwendung eines Computerprogrammes zur numerischen Modellierung von Diffusionsprofilen in Mineralkörnern
… neues Modell entwickelt. Dieses beruht auf dem Crank-Nicolson-Algorithmus und simuliert die dreidimensionale isotrope Diffusion beliebiger Elemente in einem kugelförmigen Mineral. Für die Anwendung wurden drei lithologisch unterschiedliche Probensuiten aus verschiedenen tektonischen Szenarien …
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Unsteady free convection on a horizontal circular cylinder in the presence of heat generation and radiation
… method and implicit finite difference scheme of Crank Nicolson method. The solutions obtained by those two methods are used to compare the accuracy between them with the previous studies. The presence of heat generation significantly gives effect which increased the local skin-friction coefficient, …
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High Order Finite Element Solution of Elastohydrodynamic Lubrication Problems
… components respectively. Combined with the Crank-Nicolson method and other implicit schemes for the temporal discretization, highly accurate solutions are also obtained for transient line contact problems using the high order DG method for the spatial discretization. In particular, an extra …
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Validation Studies of Single-Phase Natural Circulation Response of the Fluoride salt-cooled High-temperature Reactor (FHR)
… for an explicit (forward Euler), semi-implicit (Crank Nicolson), or fully implicit (backward Euler) solution. The models used to approximate the density integral were also modified to account for a variable mesh scheme. The code was benchmarked against the original code developed at BARC, tested …
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Non-isothermal dynamics of thin-film free-surface and channel flows of non-Newtonian nanofluids
… finite-difference method, combined with a Crank-Nicolson scheme. In addition, the effects of nanoparticles on fluid velocity, extra stresses, temperature, and thermal conductivity are explored. Comparisons of the numerical results for the nanofluids with those from the literature without …
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Complex flow and transport phenomena in porous media
… discrete scheme based on the DG method and the Crank-Nicolson method is introduced. The convergence of the scheme is proven with optimal error estimates. The second part couples the surface flow and a convection-diffusion type transport with miscible displacement in the subsurface. Initially, I …
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A fast and efficient solver for viscous-plastic sea ice dynamics
… second order discretization is achieved via the Crank Nicolson scheme and consistency is improved via a novel approach to the rheology term. More importantly, we present a significant improvement to the Jacobian approximation used in the Newton iterations, and partially form the action of the …
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