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Numerics in fluids and gravitation

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Numerics in fluids and gravitation

dc.contributor.advisor	Cordero Carrión, Isabel
dc.contributor.author	Santos Pérez, Samuel
dc.contributor.other	Departament de Matemàtiques	es_ES
dc.date.accessioned	2023-09-18T08:57:19Z
dc.date.available	2023-09-19T04:45:06Z
dc.date.issued	2023	es_ES
dc.date.submitted	15-09-2023	es_ES
dc.identifier.uri	https://hdl.handle.net/10550/89315
dc.description.abstract	In this work we face hyperbolic and elliptic systems of partial differential equations with applications from health sciences to astrophysics. Some will be framed in the context of classical mechanics and other in the Theory of Relativity. Concerning the classical sector we will solve Navier-Stokes Equations to model the blood flow in aorta trying to get some relations between geometrical features and physiological magnitudes of interest. We will also discuss the Euler Equation from both Newtonian and general relativistic approach. We will derive some theoretical results with applications in the development of numerical methods for this balance law. We will propose an improved version of a Fully Constrained Formulation of the Einstein Equations. It will preserve the local uniqueness from previous versions and posses accuracy improvements with the introduction of new variables. Some preliminary test will be carried out. On the other hand, we will introduce a new numerical method to perform the time integration of stiff balance laws. The new approach present stability properties of implicit methods dealing with stiffness but with a computation cost similar to that of an explicit method. First tests in the context of Resistive Relativistic Magnetohydrodynamics and Radiation Hydrodynamics were performed. We will finish with a new algorithm to polynomial regression in several variables with applications in simulations of neutron stars.	es_ES
dc.format.extent	270 p.	es_ES
dc.language.iso	en	es_ES
dc.subject	numerical calculus	es_ES
dc.subject	gravitation	es_ES
dc.subject	einstein equations	es_ES
dc.subject	fluid mechanics	es_ES
dc.subject	computational fluid dynamics	es_ES
dc.subject	balance laws	es_ES
dc.subject	partial differential equations	es_ES
dc.subject	numerical methods	es_ES
dc.title	Numerics in fluids and gravitation	es_ES
dc.type	doctoral thesis	es_ES
dc.subject.unesco	UNESCO::MATEMÁTICAS	es_ES
dc.subject.unesco	UNESCO::ASTRONOMÍA Y ASTROFÍSICA	es_ES
dc.embargo.terms	0 days	es_ES
dc.rights.accessRights	open access	es_ES