Using Laplace’s Equation, we can move toward solving for the Velocity Potential. Laplace’s equation states that the sum of the second-order partial derivatives of a function, with respect to the Cartesian coordinates, equals zero: In completing research about Fluid Dynamics, I gained a better understanding about the physics behind Fluid Flow and was able to study the relationship Fluid Velocity had to Laplace’s Equation and how Velocity Potential obeys this equation under ideal conditions. I found this topic to be particularly fascinating since fluid dynamics is a type of mechanical physics that we do not have a chance to explore in our curriculum and for the simple fact that modeling invisible interactions is always a cool topic to explore. One example of this showed the application of these techniques onto devices that aid in the study of ocean surface currents and allowed for more accurate modeling of fluid dynamics. Kristy Schlueter-Kuck, a Mechanical Engineer whose research focuses on the applications of coherent pattern recognition techniques to needed fields to aid in solving a variety of problems. My interest in investigating Fluid Dynamics stemmed from a lecture given on campus in early February by Dr. I used the Gauss-Seidel Method to model velocity/electric field changes using vectors that correlate to changes in velocity/electric potential which depend on the points proximity to metal conductors/walls of pipes. Also, hence model in MATLAB/Simulink is nonlinear, although generated input parameters are normal distributed, resulted histogram of simulations are not normal for that reason I used "generalized extreme value distribution", which is named as 'gev' in MATLAB.My Computational Physics final project models fluid flow by relying on the analogous relationship between Electric Potential and Velocity Potential as solved through Laplace’s Equation. Because when I compare the results of 4 simulation, fit functions of distribution for both sampling looks like each other only curve of 2nd one is smoother. I think on that way I can find more correct results on cumulative distrubution function that is related with e.g. In order to have an idea about what may distribution of simulation results look like when iteration is run infinite number of times: Instead of using resulted mean and variance after n number of simulations, I've decided to find a fit function of resulted distribution, but here n has to fullfill allowed % error. What is the best way to determine number of required simulation without know actual mean and std (in my case subjected outcome of simulation is normally distributed)? In most cases the % error of mean is less than 5% but the error of std goes up to 30%. The required number of simulation I obtain is always less than 100, but % error of mean and std compare to mean and std of entire results is not always less than 5%. In my case I run the simualtion 7500 times, and compute moving means and standard deviations for each set of 100 sampling out of the 7500 simulations. So in this way it is possible to check that the resulting mean and standard deviation of $n$ simulations represent actual mean and standard deviation with 95% confidence level. N = \left\(x)$ is the standard deviation of the resulting sampling, and $z_c$ is the confidence level coefficient (e.g., for 95% it is 1.96). My question is about the required number of simulations for Monte Carlo analysis method.Īs far as I see the required number of simulations for any allowed percentage error $E$ (e.g., 5) is
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