Smoothed particle hydrodynamics and its application to fusion-relevant magnetohydrodynamical problems
- Autores: Luis Ernesto Vela Vela
- Directores de la Tesis: Luis Raul Sánchez Fernández (dir. tes.), Joachim Ernst Geiger (codir. tes.)
- Lectura: En la Universidad Carlos III de Madrid ( España ) en 2019
- Idioma: español
- Tribunal Calificador de la Tesis: José Ramón Martín Solis (presid.), Pier Paolo Ricci (secret.), Ian Foster (voc.)
- Programa de doctorado: Programa de Doctorado en Plasmas y Fusión Nuclear por la Universidad Carlos III de Madrid
- Materias:
- Texto completo no disponible (Saber más ...)
- Resumen
SPH (Smoothed Particle Hydrodynamics) is a Lagrangian numerical method to solve the equations of hydrodynamics. It has been used by the Astrophysical community to model MHD (Magnetohydrodynamical) phenomena quite successfully. Its Lagrangian nature allows for the discretisation of the all MHD equations without the need of an underlying structured mesh.
In SPH the equation of motion is derived from a Hamiltonian formalism which endows the equations with perfect mass, momentum and energy conservation properties simultaneously, and warrantees that the particles will evolve through successive stages of minimum energy forming a glass-like (Unlike a Monte-Carlo method where the particles can become quite disordered) underlying mesh that moves with the fluid. All the physical fields of the MHD model are then defined over the moving mesh and smooth fields are constructed through an interpolation technique.
Unlike PIC codes, in an explicit time integration of the SPH equations all the fields are carried by the particles (including the Electromagnetic fields) and no matrix inversion, or preconditioning, is necessary to find the resulting forces on the particles, this important characteristic gives SPH the potential to be efficiently parallelised into many processors without the added complexity of inverting Poisson's equation in the process.
One of the most salient features of SPH is its ability to formulate all the evolution equations in Cartesian coordinates even when the system geometry is not Cartesian, this allows to tackle complex geometries, like the ones found in the latest generation of fusion-relevant machines like ITER and the Wendestein-7X, with relative simplicity.
Despite its success in simulating astrophysical plasmas, SPH has never been used to simulate laboratory plasmas, nor plasmas of fusion interest. The main result of this thesis is the EVA code, that attempts to do just that. Written in FORTRAN90, EVA is an SPH implementation of the nonlinear MHD equations with fusion geometries in mind that overcomes the three main challenges when dealing with laboratory plasmas: The presence of boundaries (flat and curved), the need for adequate boundary conditions on all MHD variables, and the construction of tailored initial conditions for arbitrarily complex density profiles and very low-levels of particle noise.
Altogether, this allows EVA to simulate MHD scenarios of fusion interest. In this thesis we present the details behind EVA's internal algorithms, we benchmark it against standard SPH tests found in the literature, and finally, we compare the obtained results of the evolution of three cylindrical plasma columns (Theta-pinch, Zeta-pinch and Screw-pinch) with the behaviour predicted by the linear theory.
The results are encouraging and the proposed future work reflects the directions that need to be followed in order to make EVA a competitive player in the simulation of realistic fusion systems in the near future.
