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Showing 1 to 15 of 15 for “"Crank-Nicholson"”.
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Influência da dissipação viscosa na transferência de calor em tubos concêntricos no escoamento turbulento
… beem solved employing the numerical method of Crank-Nicholson. The influence of the dissipation on the temperature profile is pronounced in the turbulent flow in the neighborhood of the inner and outer wall of the tube and increases in the axial direction.
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Multiple steady solutions and bifurcations in the symmetric driven cavity
… integration is a splitting method, using the Crank-Nicholson method for linear terms and the second-order Adams-Bashforth method for the non-linear terms. Spatial derivatives are evaluated with finite differences, and matrix equations are treated with SOR by lines. The results show symmetric …
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Numerical simulation of primary petroleum migration
… linear form of this equation is solved using a Crank-Nicholson finite differencing scheme, and the form of the numerical solution is compared to a steady-state solution. The effects of two non-dimensional parameters are investigated. Based on these investigations, the compressibility of the …
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Efficient Numeric Computation of a Phase Diagram in Biased Diffusion of Two Species
… coexisting regions of order and disorder. The Crank-Nicholson, nonlinear Gauss-Seidel, and GMRES algorithms used to solve the model equations are discussed. Performance enhancements and limits on convergence are considered.
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Computer simulation of carburization corrosion of nickel-base superalloys
… carburizing atmospheres. The model is based on Crank-Nicholson finite difference solution of the diffusion equation. The code also includes the ternary cross diffusion effect due to substitutional alloying elements that are preferentially oxidized. The model can treat two sets of boundary …
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A perturbation model for normal and sickle cell blood microcirculation
… disease. The model uses a finite difference, Crank-Nicholson scheme for the flow and oxygen computation, while using the level set computational method to advect the red blood cell membrane on a staggered grid. A number of initial and boundary conditions were tested in the model. The …
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An implicit numerical solution of the turbulent three-dimensional incompressible boundary-layer equations
… boundary-layer equations was developed using a Crank-Nicholson implicit finite-difference technique, with the turbulent stress terms modeled with an eddy-viscosity model obtained from mixing length theory. The method was applied to two three-dimensional flow geometries for which experimental …
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Nonlinear acoustic pulse propagation in range-dependent underwater environments
… of two numerical schemes: a finite-difference Crank-Nicholson algorithm for the linear terms of the NPE and a flux-corrected transport algorithm for the nonlinear terms. In this work, an existing implementation is extended to allow for a penetrable fluid bottom. Range-dependent environments, …
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Approximations and Object-Oriented Implementation for a Parabolic Partial Differential Equation
… in the reactor. The first method used is a Crank-Nicholson finite difference technique which tranforms the 2-D heat equation into an algebraic system of equations. For the second method, a semi-discrete method is used which transforms the partial differential equation into a system of …
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Energy loss to the soil surrounding a below-grade solar energy storage pond
… the differential equation of heat transfer. The Crank-Nicholson central difference scheme was used to solve for the time derivative. Four small ponds were constructed at the VPI & SU Swine Center, Blacksburg, Virginia, to study the effect of insulation on heat losses from a warmed water pond. The …
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Model Reduction of Nonlinear Fire Dynamics Models
… In particular, we are able to show that the Crank-Nicholson method preserves the optimality conditions, but other single-step methods do not. We further clarify the need for these discrete-time ROMs to match at infinity in order to ensure local optimality.
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Modeling and Numerical Approximations of Optical Activity in the Chemical Oxygen-Iodine Laser
The chemical oxygen-iodine laser (COIL) has several important military and industrial applications. The concern of this work is do develop a partial differential equation model describing optical behavior in the COIL. Optical behavior of the COIL has traditionally been investigated via a ray …
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Numerical Solution of Multiscale Electromagnetic Systems
… both explicit Runge-Kutta method and implicit Crank-Nicholson method are implemented for time integration. </p><p>Numerical examples and realistic cases are presented to verify that the proposed methods are non-spurious and efficient DGTD schemes.</p>
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Response Of Plasma Facing Components In Tokamaks Due To Intense Energy Deposition Using Particle-In-Cell(pic) Methods
… and moving coordinates system based on the Crank-Nicholson method and Alternating Directions Implicit Method (ADI). Currently Particle-In-Cell (PIC) methods are widely used for solving complex dynamics problems involving distorted plasma hydrodynamic problems and plasma physics. The PIC …
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Discontinuous Galerkin Based Multi-Domain Multi-Solver Technique for Efficient Multiscale Electromagnetic Modeling
… equations based DGTD framework with implicit Crank-Nicholson time integration while the physical region follows the wave equation based DGTD framework with implicit Newmark-beta time integration.</p><p>To further extend the existing hybrid methods, the hybrid FDTD-SETD-FETD method is proposed …