An Implicit Finite Difference Method for a Forced Kdv Equation

A finite difference method is developed to solve a forced KdV equation representing a surface elevation of fluid flowing on a channel with a small bump at the bottom. We indicate some difficulties in solving the equation since it has a nonlinear and third derivative terms. We present the technique in this paper to solve the equation. As the result, the numerical scheme gives solutions performing nonlinear wave-trains of water surface generated by the forcing term

Implicit Finite Difference Method for Pricing of Derivatives

Parabolic partial differential equation arise in pricing of financial derivatives. Numerical methods such as finite difference methods and monte carlo methods are used to approximate solution of this equation. In this talk, the pricing of the derivatives using the implicit method will be discussed

Navier-Stokes computations for circulation control airfoils

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows

Use of a hyperbolic grid generation scheme in simulating supersonic viscous flow about three-dimensional winged configuration

The present paper describes a numerical mesh generation technique to be used with an implicit finite difference method for simulating visous supersonic flow about low-aspect-ratio wing body configurations using a single grid strategy. The computational domain is segmented into multiple regions, with borders located in supersonic areas to avoid the otherwise costly interfacing procedure between adjacent segments. The numerical procedure is applied to calculate the turbulent flow around the shuttle orbiter and a canard projectile at supersonic free stream Mach number

A comparative study of two different numerical schemes for the simulation of nonlinear dynamics of heated falling thin films

In this research, an attempt is made to characterise qualitatively the stability and dynamics of an inclined thin liquid film under the influence of instabilities due to thermo-capillarity and evaporative effects as well as van der Waals intermolecular forces, by employing the implicit finite difference method. The results are compared with solutions obtained by the Fourier spectral method. Flow in thin films of a Newtonian liquid on an inclined plane with an adjacent passive gas layer, is well represented by the Navier-Stokes equations, equation of continuity and associated boundary conditions. Long-wave (lubrication) approximation is applied to simplify the governing equations to arrive at a nonlinear partial differential equation, called equation of evolution (EOE). The spatio-temporal evolution of the interfacial instability in the film caused by internal and/or external effects are studied by numerically solving the EOE using the implicit finite difference method. The results of the numerical simulations of our thin film model are compared with those of a similar problem solved using Fourier spectral method from the literature. Simulations show remarkable agreement in the film dynamics predicted by these two methods. The film rupture times obtained using our implicit finite difference scheme closely match with the values obtained from the Fourier spectral method within less than 1% error. This implies that the implicit finite difference method can be satisfactorily employed for the efficient numerical simulation of the thin film flows, and to decipher its nonlinear dynamics reliably

Study of effects of injector geometry on fuel-air mixing and combustion

An implicit finite-difference method has been developed for computing the flow in the near field of a fuel injector as part of a broader study of the effects of fuel injector geometry on fuel-air mixing and combustion. Detailed numerical results have been obtained for cases of laminar and turbulent flow without base injection, corresponding to the supersonic base flow problem. These numerical results indicated that the method is stable and convergent, and that significant savings in computer time can be achieved, compared with explicit methods