Finite Difference Method in Fluid Potential Function and Velocity Calculation

2021 ◽  
Vol 3 (2) ◽  
pp. 1-4
Author(s):  
Farhad Sakhaee
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Potential Function ◽  
Analytical Solutions ◽  
Difference Method ◽  
Rotational Behavior ◽  
Deterministic Solution ◽  
Implicit Finite Difference ◽  
Fluid Potential ◽  
2D Space

There is no deterministic solution for many fluid problems but by applying analytical solutions many of them are approximated. In this study an implicit finite difference method presented which solves the potential function and further expanded to drive out the velocity components in 2D-space by applying a point-by-point swiping approach. The results showed the rotational behavior of both potential function as well as velocity components while encountering central obstacle.

scholarly journals A Comparative Study between Implicit and Crank-Nicolson Finite Difference Method for Option Pricing

2020 ◽  
Vol 40 (1) ◽  
pp. 13-27
Author(s):  
Tanmoy Kumar Debnath ◽  
ABM Shahadat Hossain
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Difference Method ◽  
Finite Difference Methods ◽  
Put Option ◽  
Black Scholes ◽  
Implicit Finite Difference ◽  
Difference Methods ◽  
Crank Nicolson

In this paper, we have applied the finite difference methods (FDMs) for the valuation of European put option (EPO). We have mainly focused the application of Implicit finite difference method (IFDM) and Crank-Nicolson finite difference method (CNFDM) for option pricing. Both these techniques are used to discretized Black-Scholes (BS) partial differential equation (PDE). We have also compared the convergence of the IFDM and CNFDM to the analytic BS price of the option. This turns out a conclusion that both these techniques are fairly fruitful and excellent for option pricing. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 13-27

On the Dynamics of the Weak Fréedericksz Transition for Nematic Liquid Crystals

2016 ◽  
Vol 20 (5) ◽  
pp. 1359-1380 ◽  
Author(s):  
Peder Aursand ◽  
Gaetano Napoli ◽  
Johanna Ridder
Keyword(s):  
Liquid Crystal ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Electric Field ◽  
Excited States ◽  
Difference Method ◽  
Static Case ◽  
Director Field ◽  
Implicit Finite Difference ◽  
Anchoring Strength

AbstractWe propose an implicit finite-difference method to study the time evolution of the director field of a nematic liquid crystal under the influence of an electric field with weak anchoring at the boundary. The scheme allows us to study the dynamics of transitions between different director equilibrium states under varying electric field and anchoring strength. In particular, we are able to simulate the transition to excited states of odd parity, which have previously been observed in experiments, but so far only analyzed in the static case.

A finite-difference method for the numerical solution of the Sal’nikov thermokinetic oscillator problem

1995 ◽  
Vol 449 (1936) ◽  
pp. 255-271
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Stationary Point ◽  
Difference Method ◽  
Numerical Experiments ◽  
Euler Method ◽  
Initial Value ◽  
First Order ◽  
Highly Nonlinear ◽  
Implicit Finite Difference

A finite-difference method is developed for solving two coupled, ordinary differential equations that model a sequence of chemical reactions. The initial-value problem is highly nonlinear and involves three parameters. Various types of theoretical solution of this problem (the Sal’nikov thermokinetic oscillator problem) may be found, depending on these parameters; this is because the stationary point is surrounded by up to two limit cycles. The well-known, first-order, explicit Euler method and an implicit finite difference method of the same order are used to compute the solution. It is shown that this implicit method may, in fact, be used explicitly and extensive numerical experiments are made to confirm the superior stability properties of the alternative method.

scholarly journals Numerical Investigation of the Unsteady Flows in Hydropower Plants

2021 ◽  
pp. 1-7
Author(s):  
Roozbeh Aghamagidi ◽  
Mohammad Emami ◽  
Dariush Firooznia
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Coefficient Of Friction ◽  
Difference Method ◽  
Characteristic Method ◽  
Fast Wave ◽  
Time Step ◽  
Characteristic Lines ◽  
Implicit Finite Difference ◽  
Implicit Finite Difference Method

One of the most important hazards that threatens the stability of power plant buildings is the phenomenon of water hammer, which can occur in the Penstock pipe of a turbine due to the rapid opening and closing of a valve. Fluid Descriptive Equations in this situation, there are two hyperbolic partial nonlinear partial differential equations that are very difficult and complex to solve analytically and are possible only for very simple conditions. In this study, by examining the two numerical methods of characteristic lines and implicit finite difference with Verwy & Yu schema, which are widely used in the analysis of instabilities, their disadvantages and advantages are clearly clarified and a suitable comparison basis for use. They should be provided in different conditions in hydropower plant. The results of the characteristic method in terms of maximum and minimum pressure show more and less values than the implicit finite difference method. In the characteristic method, perturbations and fast wave fronts are presented with more accuracy than the implicit finite difference method. At points near the upstream, downstream and middle boundaries, the accuracy of the characteristic method in presenting pressure and flow fluctuations is higher than the implicit finite difference method. In the characteristic method, it is recommended not to use certain time steps and try as much as possible avoid interpolation by selecting the appropriate time step. The results of examining the amount of changes in coefficient of friction in both methods show that it is not correct to take its value constant (proportional to the value obtained in stable conditions) and coefficient of friction should be calculated in proportion to changes in velocity at different times and used in the governing equation.

Sign in / Sign up

Export Citation Format

Share Document