![]() In order to create the equation to solve for the Velocity Potential, we must first determine the first-order derivative of each function. 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. ![]() To improve the performance of your Monte Carlo simulations, you can distribute the computations to run in parallel on multiple cores using Parallel Computing Toolbox™ and MATLAB Parallel Server™.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. Running Monte Carlo Simulations in Parallel Simulink Design Optimization™ provides interactive tools to perform this sensitivity analysis and influence your Simulink model design. Monte Carlo simulations help you gain confidence in your design by allowing you to run parameter sweeps, explore your design space, test for multiple scenarios, and use the results of these simulations to guide the design process through statistical analysis. The design and testing of these complex systems involves multiple steps, including identifying which model parameters have the greatest impact on requirements and behavior, logging and analyzing simulation data, and verifying the system design. You can model and simulate multidomain systems in Simulink ® to represent controllers, motors, gains, and other components. Risk Management Toolbox™ facilitates credit simulation, including the application of copula models.įor more control over input generation, Statistics and Machine Learning Toolbox™ provides a wide variety of probability distributions you can use to generate both continuous and discrete inputs. Financial Toolbox™ provides stochastic differential equation tools to build and evaluate stochastic models. In financial modeling, Monte Carlo Simulation informs price, rate, and economic forecasting risk management and stress testing. MATLAB is used for financial modeling, weather forecasting, operations analysis, and many other applications. MATLAB ® provides functions, such as uss and simsd, that you can use to build a model for Monte Carlo simulation and to run those simulations.
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