Documentation du code de simulation numérique SUNFLUIDH

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 sunfluidh:sunfluidh_link_equations_data_set [2016/11/29 11:37]yann sunfluidh:sunfluidh_link_equations_data_set [2018/12/17 14:58] (Version actuelle)yann [Links equations & Data set] Les deux révisions précédentes Révision précédente 2018/12/17 14:58 yann [Links equations & Data set] 2018/12/17 14:56 yann [The different formulations of the Poisson's equation] 2018/12/17 14:55 yann [The different formulations of the Poisson's equation] 2018/12/17 14:55 yann [Links equations & Data set] 2018/12/17 11:09 yann 2018/12/17 11:04 yann 2018/12/17 11:02 yann [The different formulations of the Poisson's equation] 2016/11/30 14:34 yann 2016/11/30 14:31 yann [Links equations & Data set] 2016/11/30 13:31 yann 2016/11/30 13:08 yann [The different formulations of the Poisson's equation] 2016/11/30 13:07 yann 2016/11/30 13:05 yann 2016/11/30 13:04 yann 2016/11/30 12:39 yann 2016/11/30 12:39 yann 2016/11/30 12:38 yann 2016/11/29 14:54 yann 2016/11/29 14:41 yann 2016/11/29 11:37 yann 2016/11/29 10:44 yann 2016/11/29 10:43 yann 2016/11/29 10:37 yann 2016/11/29 10:27 yann 2016/11/29 10:06 yann 2016/11/29 09:59 yann créée Prochaine révision Révision précédente 2018/12/17 14:58 yann [Links equations & Data set] 2018/12/17 14:56 yann [The different formulations of the Poisson's equation] 2018/12/17 14:55 yann [The different formulations of the Poisson's equation] 2018/12/17 14:55 yann [Links equations & Data set] 2018/12/17 11:09 yann 2018/12/17 11:04 yann 2018/12/17 11:02 yann [The different formulations of the Poisson's equation] 2016/11/30 14:34 yann 2016/11/30 14:31 yann [Links equations & Data set] 2016/11/30 13:31 yann 2016/11/30 13:08 yann [The different formulations of the Poisson's equation] 2016/11/30 13:07 yann 2016/11/30 13:05 yann 2016/11/30 13:04 yann 2016/11/30 12:39 yann 2016/11/30 12:39 yann 2016/11/30 12:38 yann 2016/11/29 14:54 yann 2016/11/29 14:41 yann 2016/11/29 11:37 yann 2016/11/29 10:44 yann 2016/11/29 10:43 yann 2016/11/29 10:37 yann 2016/11/29 10:27 yann 2016/11/29 10:06 yann 2016/11/29 09:59 yann créée Ligne 1: Ligne 1: ===== Links equations & Data set ===== ===== Links equations & Data set ===== + + [[:start|Click here to come back to the previous page]] + + [[sunfluidh:sunfluidh_data_setup|Click here to go to the data-set page]] + 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's equation. The result $\phi$ corresponds to the time increment of the "dynamical" pressure (the part of the pressure associated to the dynamics) and its gradient is the velocity correction that ensures the mass conservation. \\ + * In the projection step, The mass conservation is ensured by solving a Poisson's equation. The result $\phi$ corresponds to the time increment of the "dynamical" pressure (the part of the static pressure associated to the dynamics) and its gradient is the velocity correction that ensures the mass conservation. For incompressible flows, $P_{dyn}$ is the static pressure defined up to a constant. \\ $$P_{dyn}^{n+1} = P_{dyn}^{n} + \phi$$ $$P_{dyn}^{n+1} = P_{dyn}^{n} + \phi$$ $$\vec{V}^{n+1}= \vec{V}^* - \frac{\Delta t}{\rho} \nabla \phi$$ $$\vec{V}^{n+1}= \vec{V}^* - \frac{\Delta t}{\rho} \nabla \phi$$ - For more details on the projection methods, see the document here. + **For more details on the projection methods, see the document on the numerical methods used in Sunfluidh [[sunfluidh:sunfluidh_edu_documents|(click here)]].** Ligne 15: Ligne 20: * 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's equation in respect with the problem treated. * the different formulations of the Poisson's equation in respect with the problem treated. - * the links between the equations, physical quantities and [[sunfluidh:sunfluidh_data_setup|the data set]] + * the links between the equations, physical quantities and **[[sunfluidh:sunfluidh_data_setup|the input data setup]] ** Ligne 46: Ligne 51: - [[sunfluidh:sunfluidh_data_setup|here to come back to the data-set page]] + [[sunfluidh:sunfluidh_data_setup|Click here to come back to the data-set page]] ----- ----- Ligne 59: Ligne 64: - 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 $P= P_{th}+P_{dyn}$, where $P_{th}$ is the thermodynamical pressure and $P_{dyn}$ the dynamical pressure.  $P_{th}$ is supposed to be uniform over the domain and is defined by the equation of state. $P_dyn$ is solved from the Poisson's equation (see the projection methods). + 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 $P= P_{th}+P_{dyn}$, where $P_{th}$ is the thermodynamical pressure and $P_{dyn}$ the "dynamical" pressure (part of the static pressure that contributes to the fluid motion).  $P_{th}$ is supposed to be uniform over the domain and is defined by the equation of state. $P_dyn$ is solved from the Poisson's equation (see the projection methods). Ligne 80: Ligne 85: - [[sunfluidh:sunfluidh_data_setup|here to come back to the data-set page]] + [[sunfluidh:sunfluidh_data_setup|Click here to come back to the data-set page]] ===== The different formulations of the Poisson's equation ===== ===== The different formulations of the Poisson's equation ===== Ligne 103: Ligne 108: $$\nabla \frac{1}{\rho}\cdot \nabla \Phi= \frac{ \nabla \cdot \vec{V}^* - \nabla \cdot \vec{V}^{n+1} }{\alpha \Delta t}$$ $$\nabla \frac{1}{\rho}\cdot \nabla \Phi= \frac{ \nabla \cdot \vec{V}^* - \nabla \cdot \vec{V}^{n+1} }{\alpha \Delta t}$$ - where $\nabla \cdot \vec{V}^{n+1}$ is estimated from the differential equation of state$+ where$\nabla \cdot \vec{V}^{n+1}$is estimated from the differential equation of state. [[sunfluidh:sunfluidh_data_setup|here to come back to the data-set page]] [[sunfluidh:sunfluidh_data_setup|here to come back to the data-set page]] + + + **Information on numerical methods used for solving these equations is available in the pdf document present [[ :sunfluidh:sunfluidh_full_documents | here]].** + + ===== Link between the data set & the variables in equations ===== ===== Link between the data set & the variables in equations ===== - ^ List of variables ^ Definition ^ Connections ^ + **__The knowledge of the data setup is recommanded in order to better understand the links.__** [[sunfluidh:sunfluidh_data_setup|Click here to go to the data-set page]] + + + ^ List of variables ^ Definition ^ namelists where the physical quantity is defined^ |$\rho $| the fluid density | [[sunfluidh:fluid_properties_namelist| "Fluid_Properties"]], [[sunfluidh:numerical_methods_setup_namelist| "Numerical_Methods"]] | |$\rho $| the fluid density | [[sunfluidh:fluid_properties_namelist| "Fluid_Properties"]], [[sunfluidh:numerical_methods_setup_namelist| "Numerical_Methods"]] | |$\vec{V}$| the velocity field | [[sunfluidh:velocity_initialization_namelist|"Velocity_Initialization"]], [[sunfluidh:velocity_wall_boundary_condition_setup_namelist|"Velocity_Wall_Boundary_Condition_Setup"]], [[sunfluidh:inlet_boundary_conditions_setup_namelist|"Inlet_Boundary_Condition"]], [[sunfluidh:numerical_methods_setup_namelist| "Numerical_Methods"]] | |$\vec{V}$| the velocity field | [[sunfluidh:velocity_initialization_namelist|"Velocity_Initialization"]], [[sunfluidh:velocity_wall_boundary_condition_setup_namelist|"Velocity_Wall_Boundary_Condition_Setup"]], [[sunfluidh:inlet_boundary_conditions_setup_namelist|"Inlet_Boundary_Condition"]], [[sunfluidh:numerical_methods_setup_namelist| "Numerical_Methods"]] | Ligne 118: Ligne 131: |$P_{th}$| the uniform thermodynamic pressure (low Mach number Hypothesis). Either$P_{th}=P_0$or$P_{th}= \rho.\frac{R}{M}.T $| [[sunfluidh:fluid_properties_namelist| "Fluid_Properties"]] (variable "Constant_Mass_Flow) | |$P_{th}$| the uniform thermodynamic pressure (low Mach number Hypothesis). Either$P_{th}=P_0$or$P_{th}= \rho.\frac{R}{M}.T $| [[sunfluidh:fluid_properties_namelist| "Fluid_Properties"]] (variable "Constant_Mass_Flow) | |$C_p$|the mass heat capacity of the fluid | [[sunfluidh:fluid_properties_namelist | "Fluid_Properties"]] | |$C_p$|the mass heat capacity of the fluid | [[sunfluidh:fluid_properties_namelist | "Fluid_Properties"]] | - |$\lambda$| the thermal conductivity |$ \lambda = \frac{\mu\cdot C_p}{Pr}$| + |$\lambda$| the thermal conductivity | deduced from other data with the relation$ \lambda = \frac{\mu\cdot C_p}{Pr}$| |$Pr$| the Prandtl number | [[sunfluidh:fluid_properties_namelist| "Fluid_Properties"]] | |$Pr$| the Prandtl number | [[sunfluidh:fluid_properties_namelist| "Fluid_Properties"]] | |$S_{c}$| the chemical source term in the enthalpy equation | [[sunfluidh:chemical_reactions_features_namelist|Namelist "Chemical_Reactions_Features"]] | |$S_{c}$| the chemical source term in the enthalpy equation | [[sunfluidh:chemical_reactions_features_namelist|Namelist "Chemical_Reactions_Features"]] | Ligne 128: Ligne 141: |$M$|the molecular mass (it is uniform if the fluid is homogeneous or depends on the species mass fractions) | [[sunfluidh:fluid_properties_namelist| "Fluid_Properties"]] | |$M\$ |the molecular mass (it is uniform if the fluid is homogeneous or depends on the species mass fractions) | [[sunfluidh:fluid_properties_namelist| "Fluid_Properties"]] | + [[:start|Click here to come back to the previous page]] - [[sunfluidh:sunfluidh_data_setup|here to come back to the data-set page]] + [[sunfluidh:sunfluidh_data_setup|Click here to go to the data-set page]]