sunfluidh:sunfluidh_link_equations_data_set
Différences
Ci-dessous, les différences entre deux révisions de la page.
Les deux révisions précédentesRévision précédenteProchaine révision | Révision précédente | ||
sunfluidh:sunfluidh_link_equations_data_set [2016/11/30 13:05] – yann | sunfluidh:sunfluidh_link_equations_data_set [2018/12/17 14:58] (Version actuelle) – [Links equations & Data set] yann | ||
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The code Sunfluidh solves the Navier-Stokes equations by means of an incremental projection method. | The code Sunfluidh solves the Navier-Stokes equations by means of an incremental projection method. | ||
* In the prediction step, the Navier-Stokes equations are solved in order to estimate the velocity field $\vec{V}^*$ without ensuring the mass conservation ($\nabla \cdot \vec{V}=0$ for incompressible flows or $\frac{\partial \rho}{\partial t}+\nabla \cdot (\rho\vec{V})= 0$ for low Mach number flows). | * In the prediction step, the Navier-Stokes equations are solved in order to estimate the velocity field $\vec{V}^*$ without ensuring the mass conservation ($\nabla \cdot \vec{V}=0$ for incompressible flows or $\frac{\partial \rho}{\partial t}+\nabla \cdot (\rho\vec{V})= 0$ for low Mach number flows). | ||
- | * In the projection step, The mass conservation is ensured by solving a Poisson' | + | * In the projection step, The mass conservation is ensured by solving a Poisson' |
$$ P_{dyn}^{n+1} = P_{dyn}^{n} + \phi$$ | $$ P_{dyn}^{n+1} = P_{dyn}^{n} + \phi$$ | ||
$$ \vec{V}^{n+1}= \vec{V}^* - \frac{\Delta t}{\rho} \nabla \phi$$ | $$ \vec{V}^{n+1}= \vec{V}^* - \frac{\Delta t}{\rho} \nabla \phi$$ | ||
- | For more details on the projection methods, see the document here. | + | **For more details on the projection methods, see the document |
</ | </ | ||
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* the different sets of governing equations that depend on the flow is either incompressible or dilatable (low Mach number hypothesis). | * the different sets of governing equations that depend on the flow is either incompressible or dilatable (low Mach number hypothesis). | ||
* the different formulations of the Poisson' | * the different formulations of the Poisson' | ||
- | * the links between the equations, physical quantities and [[sunfluidh: | + | * the links between the equations, physical quantities and **[[sunfluidh: |
</ | </ | ||
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</ | </ | ||
- | [[sunfluidh: | + | [[sunfluidh: |
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<note important> | <note important> | ||
- | We remind the user that the low Mach hypothesis is based on the hypothesis of the scale splitting between the thermodynamics and dynamics phenomena. As a consequence the pressure is read as $P= P_{th}+P_{dyn}$, | + | We remind the user that the low Mach hypothesis is based on the hypothesis of the scale splitting between the thermodynamics and dynamics phenomena. As a consequence the pressure is read as $P= P_{th}+P_{dyn}$, |
</ | </ | ||
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</ | </ | ||
- | [[sunfluidh: | + | [[sunfluidh: |
===== The different formulations of the Poisson' | ===== The different formulations of the Poisson' | ||
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$$ \nabla \frac{1}{\rho}\cdot \nabla \Phi= \frac{ \nabla \cdot \vec{V}^* - \nabla \cdot \vec{V}^{n+1} }{\alpha \Delta t} $$ | $$ \nabla \frac{1}{\rho}\cdot \nabla \Phi= \frac{ \nabla \cdot \vec{V}^* - \nabla \cdot \vec{V}^{n+1} }{\alpha \Delta t} $$ | ||
- | where $\nabla \cdot \vec{V}^{n+1}$ is estimated from the differential equation of state$ | + | where $\nabla \cdot \vec{V}^{n+1}$ is estimated from the differential equation of state. |
[[sunfluidh: | [[sunfluidh: | ||
+ | |||
+ | <WRAP info> | ||
+ | **Information on numerical methods used for solving these equations is available in the pdf document present [[ : | ||
+ | </ | ||
+ | |||
===== Link between the data set & the variables in equations ===== | ===== Link between the data set & the variables in equations ===== | ||
- | **__The knowledge of the data setup is recommanded in order to better understand the links.__** | + | **__The knowledge of the data setup is recommanded in order to better understand the links.__** |
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[[: | [[: | ||
- | [[sunfluidh: | + | [[sunfluidh: |
sunfluidh/sunfluidh_link_equations_data_set.1480507511.txt.gz · Dernière modification : 2016/11/30 13:05 de yann