AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code
A two-dimensional axisymmetric implementation of the smoothed particle hydrodynamics (SPH) technique, called for short AxisSPH, has been described in this thesis, along with a number of basic tests and realistic applications. The main goal of this work was to fill a gap on a topic which has been sca...
| Author: | |
|---|---|
| Format: | doctoral thesis |
| Publication Date: | 2012 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/94616 |
| Online Access: | https://hdl.handle.net/2117/94616 https://dx.doi.org/10.5821/dissertation-2117-94616 |
| Access Level: | Open access |
| Keyword: | hidrodinàmica mètodes numèrics smoothed particle hydrodynamics (SPH) inertial confinement fusion (ICF) Supernova Hidrodinàmica -- Mètodes numèrics Simetria (Física) Dinàmica de fluids Fusió nuclear Supernoves Física nuclear Àrees temàtiques de la UPC::Física |
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AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code |
| title |
AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code |
| spellingShingle |
AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code Relaño Castillo, Antonio hidrodinàmica mètodes numèrics smoothed particle hydrodynamics (SPH) inertial confinement fusion (ICF) Supernova Hidrodinàmica -- Mètodes numèrics Simetria (Física) Dinàmica de fluids Fusió nuclear Supernoves Física nuclear Àrees temàtiques de la UPC::Física |
| title_short |
AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code |
| title_full |
AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code |
| title_fullStr |
AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code |
| title_full_unstemmed |
AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code |
| title_sort |
AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics code |
| dc.creator.none.fl_str_mv |
Relaño Castillo, Antonio |
| author |
Relaño Castillo, Antonio |
| author_facet |
Relaño Castillo, Antonio |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
García Senz, Domingo |
| dc.subject.none.fl_str_mv |
hidrodinàmica mètodes numèrics smoothed particle hydrodynamics (SPH) inertial confinement fusion (ICF) Supernova Hidrodinàmica -- Mètodes numèrics Simetria (Física) Dinàmica de fluids Fusió nuclear Supernoves Física nuclear Àrees temàtiques de la UPC::Física |
| topic |
hidrodinàmica mètodes numèrics smoothed particle hydrodynamics (SPH) inertial confinement fusion (ICF) Supernova Hidrodinàmica -- Mètodes numèrics Simetria (Física) Dinàmica de fluids Fusió nuclear Supernoves Física nuclear Àrees temàtiques de la UPC::Física |
| description |
A two-dimensional axisymmetric implementation of the smoothed particle hydrodynamics (SPH) technique, called for short AxisSPH, has been described in this thesis, along with a number of basic tests and realistic applications. The main goal of this work was to fill a gap on a topic which has been scarcely addressed in the published literature concerning SPH. Although the application of AxisSPH to the simulation of real problems is restricted to those systems which display the appropriate symmetry there are, however, many interesting examples of physical systems which evolve following the axisymmetric premise. These examples belong to a variety of scientific and technological areas such as, for example, astrophysics, laboratory astrophysics or inertial confinement fusion. Additionally AxisSPH can be also useful in convergence studies of the standard 3D-SPH technique because the higher resolution achieved in 2D can be used to benchmark the three-dimensional codes. The main improvements implemented in AxisSPH with respect existing axisymmetric SPH formulations are summarized as follows: 1) We have derived simple analytical expressions for correction factors which largely improves the calculation of density and velocity in the vicinity of the z-axis. These expressions and their derivatives were given as a function of an adimensional parameter and do not increase the computational load of the scheme. 2) We have obtained the appropriate expression of the fluid Euler equations containing the new correction functions and their derivatives. Far enough from the singular axis, the scheme reduces to the standard formulation discussed by Brookshaw (2003). 3) A novel expression for the heat conduction term, which has to be added to the energy equation was devised and checked. This new term improves the description of the heat flux for those particles located at the axis neighborhoods. 4) Until now axisymmetric SPH hydrocodes handle artificial viscosity using a crude approach because it was treated as a simple restriction of the standard 3D Cartesian viscosity to 2D. Here we propose to calculate the viscous pressure as a combination of two terms, the first one is the (standard) Cartesian part and the second is the axis-converging part of the viscosity respectively. As expected this last term is of special relevance to simulate implosions. 5) We have developed an original method to incorporate gravity into AxisSPH. First the direct ring to ring force was found as a function of the Euclidean distance between the 2D particles. In second place the gravitational force on a given particle was obtained by summing the contributions of all N particles. We have also developed a more efficient scheme to obtain the gravitational force calculating the potential of the ring, instead the force because it involves lesser algebraic operations. The scheme has been checked using a large number of tests cases. These tests range from very specific oriented to check a particular algorithm or a piece of physics, to rather complex ones intended to analyze the behavior of the scheme in potential real applications (ICF, jets, astrophysics). At least in one case, the head on collision of a pair of white dwarfs, the result of the simulations carried out using AxisSPH brings new, unpublished, scientific material. |
| publishDate |
2012 |
| dc.date.none.fl_str_mv |
2012 2012-06-06 2012 2012-07-09 |
| dc.type.none.fl_str_mv |
doctoral thesis http://purl.org/coar/resource_type/c_db06 VoR http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
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https://hdl.handle.net/2117/94616 https://dx.doi.org/10.5821/dissertation-2117-94616 |
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https://hdl.handle.net/2117/94616 https://dx.doi.org/10.5821/dissertation-2117-94616 |
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Inglés eng |
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Inglés |
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eng |
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open access http://purl.org/coar/access_right/c_abf2 |
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info:eu-repo/semantics/openAccess |
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open access http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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application/pdf |
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Universitat Politècnica de Catalunya |
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Universitat Politècnica de Catalunya |
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reponame:UPCommons. Portal del coneixement obert de la UPC instname:Universitat Politècnica de Catalunya (UPC) |
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Universitat Politècnica de Catalunya (UPC) |
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UPCommons. Portal del coneixement obert de la UPC |
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AxisSPH:devising and validating an axisymmetric smoothed particle hydrodynamics codeRelaño Castillo, Antoniohidrodinàmicamètodes numèricssmoothed particle hydrodynamics (SPH)inertial confinement fusion (ICF)SupernovaHidrodinàmica -- Mètodes numèricsSimetria (Física)Dinàmica de fluidsFusió nuclearSupernovesFísica nuclearÀrees temàtiques de la UPC::FísicaA two-dimensional axisymmetric implementation of the smoothed particle hydrodynamics (SPH) technique, called for short AxisSPH, has been described in this thesis, along with a number of basic tests and realistic applications. The main goal of this work was to fill a gap on a topic which has been scarcely addressed in the published literature concerning SPH. Although the application of AxisSPH to the simulation of real problems is restricted to those systems which display the appropriate symmetry there are, however, many interesting examples of physical systems which evolve following the axisymmetric premise. These examples belong to a variety of scientific and technological areas such as, for example, astrophysics, laboratory astrophysics or inertial confinement fusion. Additionally AxisSPH can be also useful in convergence studies of the standard 3D-SPH technique because the higher resolution achieved in 2D can be used to benchmark the three-dimensional codes. The main improvements implemented in AxisSPH with respect existing axisymmetric SPH formulations are summarized as follows: 1) We have derived simple analytical expressions for correction factors which largely improves the calculation of density and velocity in the vicinity of the z-axis. These expressions and their derivatives were given as a function of an adimensional parameter and do not increase the computational load of the scheme. 2) We have obtained the appropriate expression of the fluid Euler equations containing the new correction functions and their derivatives. Far enough from the singular axis, the scheme reduces to the standard formulation discussed by Brookshaw (2003). 3) A novel expression for the heat conduction term, which has to be added to the energy equation was devised and checked. This new term improves the description of the heat flux for those particles located at the axis neighborhoods. 4) Until now axisymmetric SPH hydrocodes handle artificial viscosity using a crude approach because it was treated as a simple restriction of the standard 3D Cartesian viscosity to 2D. Here we propose to calculate the viscous pressure as a combination of two terms, the first one is the (standard) Cartesian part and the second is the axis-converging part of the viscosity respectively. As expected this last term is of special relevance to simulate implosions. 5) We have developed an original method to incorporate gravity into AxisSPH. First the direct ring to ring force was found as a function of the Euclidean distance between the 2D particles. In second place the gravitational force on a given particle was obtained by summing the contributions of all N particles. We have also developed a more efficient scheme to obtain the gravitational force calculating the potential of the ring, instead the force because it involves lesser algebraic operations. The scheme has been checked using a large number of tests cases. These tests range from very specific oriented to check a particular algorithm or a piece of physics, to rather complex ones intended to analyze the behavior of the scheme in potential real applications (ICF, jets, astrophysics). At least in one case, the head on collision of a pair of white dwarfs, the result of the simulations carried out using AxisSPH brings new, unpublished, scientific material.En esta tesis se ha desarrollado un código, que hemos llamado AxisSPH, en dos dimensiones axisimétrico a partir de la técnica conocida como SPH (“smooothed particle hydrodynamics”). AxisSPH ha sido validado después de realizar una serie de tests básicos y algunas simulaciones de situaciones reales. El objetivo principal de este trabajo ha sido llenar, en parte, el vacío existente al respecto en la literatura sobre SPH. Aunque sólo se puede aplicar AxisSPH en problemas reales que presenten la apropiada simetría, existen muchos ejemplos interesantes de sistemas físicos que presentan la simetría axial demandada. Existen ejemplos en campos de aplicación tanto científica como tecnológica, por ejemplo en astrofísica, en el llamado laboratorio de astrofísica o en fusión por confinamiento inercial (ICF). Otra interesante aplicación de AxisSPH puede ser su utilización en estudios de convergencia con otros códigos 3D-SPH debido a su mayor resolución, al tratarse de un código 2D. Las mejoras implementadas en el código AxisSPH en comparación con otros códigos axisimétricos SPH existentes se pueden resumir en los siguientes puntos: 1) Hemos deducido expresiones analíticas simples para unos factores de corrección que mejoran el cálculo de la densidad y la velocidad en las proximidades del eje z. Dichas expresiones y sus derivadas dependen de un parámetro adimensional que no incrementa mucho el peso computacional del esquema propuesto. 2) Hemos obtenido las expresiones adecuadas de las ecuaciones de Euler que contienen estas nuevas funciones correctoras y sus derivadas. Lejos del eje de singularidad estas ecuaciones se transforman en las de la formulación estándar propuesta por Brookshaw (2003). 3) Una expresión novedosa del término de conducción, que debe de añadirse a la ecuación de la energía, se ha propuesto y validado. Este nuevo término mejora la evolución del flujo de calor de las partículas situadas en las proximidades del eje z. 4) Hasta el momento los códigos hidrodinámicos SPH axisimétricos existentes trabajaban con una aproximación poco elaborada de la viscosidad artificial ya que consistían en una restricción a dos dimensiones de la viscosidad estándar 3D. En este trabajo proponemos el cálculo de la presión debida a la viscosidad como combinación de dos términos, el primero reflejo de la parte cartesiana y la segunda da cuenta de la parte relacionada con la convergencia en el eje. Como era de esperar este último término es de relevante importancia en la simulación de implosiones. 5) Hemos desarrollado un método original para incorporar el cálculo de la gravedad en el código AxisSPH. En primer lugar la fuerza directa de anillo a anillo y en segundo lugar la fuerza de la gravedad que sufre una determinada partícula a partir de la contribución del resto de las N partículas existentes. También hemos desarrollado un esquema más eficiente para calcular la gravedad a partir del cálculo del potencial del anillo en lugar del cálculo directo de la fuerza ya que implica un menor número de operaciones algebraicas. El método ha sido verificado con un gran número de test numéricos. Desde los más específicos orientados a comprobar la validez de un algoritmo particular o la capacidad para simular un fenómeno físico en particular, hasta simulaciones bastante más complejas, con la intención de validar la capacidad de simular aplicaciones potencialmente más reales (ICF, jets, astrofísica). Así, en al menos un caso, en la colisión frontal de dos enanas blancas, los resultados de la simulación utilizando AxisSPH pueden aportar material científico publicable.Universitat Politècnica de CatalunyaGarcía Senz, Domingo20122012-06-0620122012-07-09doctoral thesishttp://purl.org/coar/resource_type/c_db06VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/doctoralThesisapplication/pdfhttps://hdl.handle.net/2117/94616https://dx.doi.org/10.5821/dissertation-2117-94616reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/946162026-05-27T15:37:01Z |
| score |
15,301603 |