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FengChen

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Why study Modelica

I have seen a book “Model Thinking” before, and this time it happens to be in the CoVid-2019 disease ravaging the world, by chance I saw the prediction model SEIR about epidemiology, I took this opportunity to start studying mathematical models, and decided to pick up the mathematical analysis, ordinary differential equations, partial differential equations, differential geometry and other courses I studied in college. I came across the language Modelica, and since I had been studying Wolfram Mathematica, I was quite fond of SystemModeler of the Wolfram product line, so I started to buy the home edition of SystemModeler and purchased a book “Introduction and Improvement of Modelica Multi-Domain Physical System Modeling”. I began my exploration of Modelica with the expectation of gaining a deeper understanding of mathematical model building, using mathematical models to predict the future development pattern of an event and gaining more hidden information in quantitative data analysis.

Modeling - Hydraulic Systems

The language used is Mathematica.

HydraulicSystem

The fluid is incompressible

First build a system of equations based on the Hagen-Poiseuille relationship: 1 2

3 4

5 6

Pre-set parameters: 7 8

Assuming that the cross-sectional area of the tubes on both sides is the same as 1 9

Solve the above differential equation 10

Plots of height change of h1, h2 h1[t], h2[t] 11 12

The set of equations is shown below: 13-1

13

Finally, create the SystemModeler model 14

model W8918fcdd72d8462a890fa97776822164
  parameter Real g = 9.81;
  parameter Real mu = 1 / 500;
  parameter Real pipeDia = 0.2;
  parameter Real pipeLen = 0.1;
  parameter Real rho = 0.2;
  Real h1;
  Real h2;
  Real p1;
  Real p2;
initial equation
  h1 = 1;
  h2 = 0;
equation
  p1 = g * rho * h1;
  p2 = g * rho * h2;
  der(h1) = (-1) / 128 * Modelica.Constants.pi * pipeDia ^ 4 * pipeLen ^ (-1) * mu ^ (-1) * (p1 + (-1) * p2);
  der(h2) = 1 / 128 * Modelica.Constants.pi * pipeDia ^ 4 * pipeLen ^ (-1) * mu ^ (-1) * (p1 + (-1) * p2);
";
end W8918fcdd72d8462a890fa97776822164;

Copy the Modelica source code to SystemModeler and run it to get the following graph of h1, h2 height change 15

Summary

In the absence of Mathematica and SystemModeler combined use, for the first stage of rapid writing Modelica source code is a tricky thing, then check the Mathematica help documentation found that you can use CreateSystemModel to complete the automatic generation of code, the advantage is that you can completely The advantage is that you can create intuitive mathematical logic in Mathematica, and then automatically generate Modelica code by CreateSystemModel and put it into modeler for further analysis and processing.

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不断的学习思考, 保持好奇心
Keep thinking, Stay curious
始终保持对于新事物的敏感
Always be sensitive to new things