SEMI LAGRANGIAN METHOD FOR HYPERBOLIC TYPE EQUATIONS
Most of fundamental equations in fluid dynamics can be derived from first principles in either a Lagrangian form or an Eulerian form. Different from Eulerian equations <br /> <br /> <br /> <br /> <br /> <br /> <br /> that describe the evolution obs...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/15733 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Most of fundamental equations in fluid dynamics can be derived from first principles in either a Lagrangian form or an Eulerian form. Different from Eulerian equations <br />
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that describe the evolution observed at a fixed point, Lagrangian equations describe the evolution of the flow that would be observed following the motion of an individual parcel of fluid. A standard numerical method for solving Lagrangian type of equations is the Euler method, Runge-Kutta method, or Heun method. But this numerical approximation becomes inaccurate in regions where the fluid parcels are widely separated. This final projects discussed another method called the semi Lagrangian method. In this method, spatial domain is equally partitions, with fixed <br />
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grid points. And the idea is main value at current position of the fluid parcel at any time is interpolated using known values at grid points. In this final project the semi <br />
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Lagrangian method is implemented to solve transport equations, Burger equations and shallow water equations (SWE). The advantage of this method is unconditionally <br />
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stable. |
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