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Showing 1 to 15 of 15 for “"Finite difference equations"”.
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Variational derivation of modal-nodal finite difference equations in spatial reactor physics.
Massachusetts Institute of Technology. Dept. of Nuclear Engineering. Thesis. 1972. Ph.D.
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A New Method for Treating Wells in Reservoir Simulation
<p>A new method for formulating finite difference equations for reservoir simulation has been developed. It can be applied throughout the entire simulated reservoir or to local segments. When applied to cells containing vertical, fully penetrating, straight-line wells in a homogeneous reservoir, …
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An implicit numerical solution for the laminar and turbulent flow of an incompressible fluid along the axis of a 90-degree corner
A method of solving the equations for the three–dimensional, incompressible laminar and turbulent flow along the intersection of two planes at ninety-degrees has been developed. The Alternating Direction Implicit (ADI) finite-difference method was applied for both types of flow. The turbulent …
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A New Method for the Rapid Calculation of Finely-Gridded Reservoir Simulation Pressures
… requiring millions of cells using traditional finite-difference equations with only hundreds of cells. This was accomplished through the use of finite-difference equations that incorporate the physics of the flow. Although these coarse-grid solutions achieve accuracies normally requiring orders …
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Calculation of the flow over a stalled airfoil
… regions of separated flow, is presented. The finite-difference equations resulting from an integral method for the laminar and turbulent boundary layers are solved simultaneously in a line-relaxation procedure with the equations for the outer, inviscid flow. These coupled equations allow …
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An implicit numerical solution of the turbulent three-dimensional incompressible boundary-layer equations
… incompressible turbulent 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 …
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The stability of linear operators
… of both ordinary and partial differential equations by finite difference equations, it is well-known that for different ratios of the time interval to the spatial intervals widely differing solutions are obtained. This problem was first attacked by John von Neumann using Fourier analysis. …
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Lie group invariant finite-difference schemes for the neutron diffusion equation
Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference …
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Effect of membrane weight on vibrations of air-inflated dams
… of the membrane was negligible. In this study, equations of equilibrium and equations of motion were derived for an air inflated dam impounding no water, but loaded with its own membrane weight. It was assumed that the effect of membrane extensibility is negligible in the analysis. Derivatives …
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Laser Annealing of Ion Implanted Silicon
… calculations we have used the technique of finite difference equations to solve the one-dimensional heat conduction equations for the solid and liquid phases. We have taken into account the temperature dependence of all the parameters involved to give us a realistic model. The melting model …
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Transient state analysis of separated flow around a sphere
… falling sphere was calculated by considering the difference between the gravitational force and the drag force in a transient state. The governing partial differential equations were non-dimensionalized. A set of implicit finite difference equations was developed. In order to obtain accurate …
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Three-Dimensional Finite Difference Analysis of Geosynthetic Reinforcement Used in Column-Supported Embankments
… energy was then applied, utilizing central finite difference equations. Energy components from vertical loading, soil and column support, as well as bending and membrane stiffness of the geosynthetic are considered. Three pile orentation types were implemented: square piles, circular piles, …
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Experimental and predicted performance for the combustion of a low heating value gas in a swirl burner
… The investigation covers the development of a finite difference analysis of the flow and combustion processes in such a burner. In conjunction with the analytical work, an experimental program was conducted to provide detailed measurements of the three-dimensional velocity distributions within …
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The mathematical modelling and numerical solution of options pricing problems
… pricing problems. The methods are based on finite difference discretisation coupled with optimal solvers of the resulting discrete systems. Regular Cartesian meshes have been combined with orthogonal co-ordinate transformations chosen for numerical accuracy rather than reduction of the …
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Three dimensional heterogeneous finite element method for static multi-group neutron diffusion
… heterogeneity. A three-dimensional Heterogeneous Finite Element Method (HFEM) is developed to address the limitations of current methods by offering fine-group energy representation and fuel-pin-level spatial detail at modest computational cost. The calculational cost of the method is roughly …