Coupling marker and cell and smoothed particle hydrodynamics for fluid animation

• Autores: Nuria Suarez de la Torre
• Directores de la Tesis: Antoni Susín Sánchez (dir. tes.), Carlos García Gómez (dir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2006
• Idioma: español
• Tribunal Calificador de la Tesis: Amadeu Delshams i Valdés (presid.), Pere Brunet Crosa (secret.), Renato Pajarola (voc.), Oscar GarCiA-Panyella (voc.), John Hogan (voc.)
• Materias:
  • Matemáticas
    • Ciencia de los ordenadores
      • Simulación
    • Análisis numérico
      • Ecuaciones diferenciales
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• Resumen

  • In the physically-based fluid animation world, one of the most important challenges is the solution of the Navier-Stokes equations, To solve them in an animation framework, the desired method should be fast, catch all the details of the fluid movement (e.g. splash) and maintain some capability to be manipulated by the animator, making possible the creation of scenes even if they are not physically correct. Often using just one method is not a good solution, mainly because of the complicated behaviour of fluids. In this work we present a coupling method that works trying to profit from the advantages of the two most widely used methods in fluid simulation and to avoid their disadvantages. These methods are:

    - Smoothed Particles Hydrodynamics (SPH): As a Lagrangian approach, the fluid is supposed to be composed by particles. Each of them has its own material characteristics which are determined by means of kernel functions that define their local influence. This method has very high-level detail but it is really slow and computationally expensive, since the behaviour of every particle depends on its neighbours at every moment.

    - Marker and Cell (MAC): As Eulerian approach, the fluid values (pressure and velocities) are calculated over a meshed simulation domain. The position of the fluid is determined by marker particles, moved according to the velocity field. Although it needs an iterative system to solve for pressures, it can be considered a fast simulation method, but tends to make features smoother than they are, achieving lower level of detail than SPH.

    Thus, if we face the problem of simulating a big bulk of fluid where the events needing high-level detail happen near the surface (e.g. a swimming pool or a bath) it seems very appropriated to combine both methods. We have done exactly this: we have studied MAC and SPH in detail and constructed our own algorithms for them; then we have coupled them using MAC for the internal part of the fluid (smoother and more