add new models

Author: ratnania

_toc.yml

@@ -72,29 +72,102 @@ parts:
     chapters:
       - file: chapter5/cfd
         sections:
-          - file: chapter5/buoyancy-driven_natural_convection         
-          - file: chapter5/compressible_flow_in_a_nozzle              
-          - file: chapter5/convection-diffusion_equation_in_a_channel 
-          - file: chapter5/free_surface_flow                          
-          - file: chapter5/heat_conduction_in_a_solid                 
-          - file: chapter5/incompressible_flow_past_a_cylinder        
-          - file: chapter5/magnetohydrodynamics_flow                  
-          - file: chapter5/particle-laden_flow                        
-          - file: chapter5/stokes_flow_in_a_lid-driven_cavity         
-          - file: chapter5/two-phase_flow                             
-          - file: chapter5/non-newtonian-fluids
-            sections:
-              - file: chapter5/power_law_fluid_flow_in_a_channel          
-              - file: chapter5/bingham_plastic_flow_in_a_pipe             
-              - file: chapter5/oldroyd-b_fluid_flow_in_a_channel          
-              - file: chapter5/herschel-bulkley_fluid_flow_in_a_pipe      
-              - file: chapter5/cross_power_law_fluid_flow_in_a_channel    
-              - file: chapter5/casson_fluid_flow_in_a_channel             
-              - file: chapter5/papanastasiou_fluid_flow_in_a_channel      
+          - file: chapter5/cfd/buoyancy-driven_natural_convection         
+          - file: chapter5/cfd/compressible_flow_in_a_nozzle              
+          - file: chapter5/cfd/convection-diffusion_equation_in_a_channel 
+          - file: chapter5/cfd/free_surface_flow                          
+          - file: chapter5/cfd/heat_conduction_in_a_solid                 
+          - file: chapter5/cfd/incompressible_flow_past_a_cylinder        
+          - file: chapter5/cfd/magnetohydrodynamics_flow                  
+          - file: chapter5/cfd/particle-laden_flow                        
+          - file: chapter5/cfd/stokes_flow_in_a_lid-driven_cavity         
+          - file: chapter5/cfd/two-phase_flow                             
+          - file: chapter5/cfd/non-newtonian-fluids
+            sections:      
+              - file: chapter5/cfd/power_law_fluid_flow_in_a_channel          
+              - file: chapter5/cfd/bingham_plastic_flow_in_a_pipe             
+              - file: chapter5/cfd/oldroyd-b_fluid_flow_in_a_channel          
+              - file: chapter5/cfd/herschel-bulkley_fluid_flow_in_a_pipe      
+              - file: chapter5/cfd/cross_power_law_fluid_flow_in_a_channel    
+              - file: chapter5/cfd/casson_fluid_flow_in_a_channel             
+              - file: chapter5/cfd/papanastasiou_fluid_flow_in_a_channel      
       - file: chapter5/fsi
+        sections:
+          - file: chapter5/fsi/flutter_analysis_of_a_flexible_wing_in_fluid_flow
+          - file: chapter5/fsi/two-way_fluid-structure_interaction_in_a_tube
+          - file: chapter5/fsi/fluid-structure_interaction_in_a_flexible_channel
       - file: chapter5/electromagnetics
       - file: chapter5/mhd
+        sections:
+          - file: chapter5/mhd/mhd-stability-analysis
+            sections:
+              - file: chapter5/mhd/mhd_rayleigh-taylor_instability_in_a_conducting_fluid
+              - file: chapter5/mhd/mhd_kelvin-helmholtz_instability_in_magnetized_flows
+              - file: chapter5/mhd/mhd_stability_of_a_current-carrying_plasma_column
+          - file: chapter5/mhd/mhd-turbulence
+            sections:
+              - file: chapter5/mhd/mhd_turbulence_in_solar_winds
+              - file: chapter5/mhd/mhd_turbulence_in_laboratory_plasmas
+              - file: chapter5/mhd/mhd_turbulence_in_accretion_disks
+          - file: chapter5/mhd/mhd-heat-transfer
+            sections:
+              - file: chapter5/mhd/mhd_heat_transfer_in_a_rectangular_domain
+              - file: chapter5/mhd/mhd_heat_transfer_in_a_cylindrical_fusion_reactor
+              - file: chapter5/mhd/mhd_heat_transfer_in_a_magma_convection_model
+          - file: chapter5/mhd/mhd-dynamo
+            sections:
+              - file: chapter5/mhd/simple_kinematic_dynamo_model
+              - file: chapter5/mhd/mhd_dynamo_in_a_rotating_sphere
+              - file: chapter5/mhd/astrophysical_dynamo_in_a_stellar_interior
+          - file: chapter5/mhd/mhd-astrophysics
+            sections:
+              - file: chapter5/mhd/mhd_star_formation_in_a_protostellar_cloud
+              - file: chapter5/mhd/mhd_solar_wind_simulation
+              - file: chapter5/mhd/mhd_accretion_disk_in_binary_star_system
+          - file: chapter5/mhd/mhd-material-processing
+            sections:
+              - file: chapter5/mhd/mhd_aluminum_electromagnetic_stirring
+              - file: chapter5/mhd/mhd_continuous_casting_of_steel
+              - file: chapter5/mhd/mhd_metal_solidification_in_magnetic_field
+          - file: chapter5/mhd/mhd-drug-targeting
+            sections:
+              - file: chapter5/mhd/magnetic_targeting_in_a_blood_vessel
+              - file: chapter5/mhd/magnetic_targeting_in_tumor_tissue
+              - file: chapter5/mhd/magnetic_targeting_in_the_eye_for_retinal_diseases
+          - file: chapter5/mhd/mhd-fluid-dynamics
+            sections:
+              - file: chapter5/mhd/ferrofluid_flow_in_a_microfluidic_device
+              - file: chapter5/mhd/ferrofluid_damper_in_mechanical_system
+              - file: chapter5/mhd/magnetic_fluid_actuator_in_valve_control
+          - file: chapter5/mhd/mhd-fusion
       - file: chapter5/material-science
+        sections:
+          - file: chapter5/material-science/creep_in_viscoelastic_materials
+          - file: chapter5/material-science/diffusion_and_reaction_in_porous_media
+          - file: chapter5/material-science/elasticity_with_thermal_expansion
+          - file: chapter5/material-science/heat_conduction_with_phase_change
+          - file: chapter5/material-science/piezoelectric_material
+          - file: chapter5/material-science/composite-materials
+            sections:      
+              - file: chapter5/material-science/homogenization_of_composite_structures
+              - file: chapter5/material-science/thermal_conductivity_of_composite_materials
+              - file: chapter5/material-science/fiber-reinforced_composite_materials
+              - file: chapter5/material-science/composite_materials_with_piezoelectric_fibers
+              - file: chapter5/material-science/composite_materials_with_thermal_expansion
+          - file: chapter5/material-science/composite-materials-analysis
+            sections:      
+              - file: chapter5/material-science/laminate_plate_bending
+              - file: chapter5/material-science/composite_beam_analysis
+              - file: chapter5/material-science/composite_pressure_vessel_analysis
+              - file: chapter5/material-science/composite_shaft_analysis
+              - file: chapter5/material-science/composite_shell_structures
+          - file: chapter5/material-science/additive-manifacturing
+            sections:      
+              - file: chapter5/material-science/thermal_simulation_in_powder_bed_fusion
+              - file: chapter5/material-science/fluid_flow_simulation_in_directed_energy_deposition
+              - file: chapter5/material-science/structural_simulation_in_fused_filament_fabrication
+              - file: chapter5/material-science/multi-material_simulation_in_material_jetting
+              - file: chapter5/material-science/residual_stress_simulation_in_selective_laser_melting
       - file: chapter5/multiphysics
   - caption: Documentation
     chapters:

chapter5/bingham_plastic_flow_in_a_pipe.ipynb chapter5/cfd/bingham_plastic_flow_in_a_pipe.ipynb

@@ -46,12 +46,5 @@ To apply the finite element method, the domain $\Omega$ is discretized into elem
 
 ## References
 
-The following references provide in-depth coverage of the mathematical background for electromagnetism using finite elements:
+The following references provide in-depth coverage of the mathematical background for electromagnetism using finite elements: {cite}`jin2015finite`  {cite}`bossavit1998whitney` {cite}`monk2003finite`
 
-\begin{enumerate}
-    \item \cite{jin2015finite} 
-    \item \cite{bossavit1998whitney}
-    \item \cite{monk2003finite}
-\end{enumerate}
-
-This mathematical background serves as the foundation for implementing finite element simulations of electromagnetic problems. Researchers interested in detailed mathematical derivations and computational techniques are encouraged to explore the referenced works.

chapter5/buoyancy-driven_natural_convection.ipynb chapter5/cfd/buoyancy-driven_natural_convection.ipynb

@@ -7,11 +7,13 @@ Fluid-Structure Interaction (FSI) involves the coupled interaction between a flu
 
 The governing equations for fluid-structure interaction involve the Navier-Stokes equations for the fluid and the equations of motion for the structure. In a partitioned approach, the coupled system is given by:
 
+$$
 \begin{align}
     \text{Fluid Domain:} \quad \rho_f \left(\frac{\partial \mathbf{u}_f}{\partial t} + (\mathbf{u}_f \cdot \nabla)\mathbf{u}_f\right) &= -\nabla p_f + \mu_f \nabla^2 \mathbf{u}_f + \mathbf{f}_f + \mathbf{F}_s, \label{eq:fsi_fluid_momentum} \\
     \nabla \cdot \mathbf{u}_f &= 0, \label{eq:fsi_fluid_continuity} \\
     \text{Structure Domain:} \quad \rho_s \frac{\partial^2 \mathbf{u}_s}{\partial t^2} &= \nabla \cdot \mathbf{P}_s + \mathbf{f}_s, \label{eq:fsi_structure_motion}
 \end{align}
+$$
 
 where:
 
@@ -65,12 +67,4 @@ The coupling conditions, such as \eqref{eq:fsi_kinematic_condition} and \eqref{e
 
 ## References
 
-The following references provide comprehensive coverage of the mathematical background for fluid-structure interaction using finite elements:
-
-\begin{enumerate}
-    \item \cite{hron2006fluid}  
-    \item \cite{bathe2014finite}
-    \item \cite{quarteroni2017fluid}
-\end{enumerate}
-
-Researchers interested in detailed mathematical derivations and computational techniques are encouraged to explore the referenced works.
+The following references provide comprehensive coverage of the mathematical background for fluid-structure interaction using finite elements: {cite}`hron2006fluid`  {cite}`bathe2014finite` {cite}`quarteroni2017fluid`

chapter5/casson_fluid_flow_in_a_channel.ipynb chapter5/cfd/casson_fluid_flow_in_a_channel.ipynb

@@ -0,0 +1,94 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "c06958bc",
+   "metadata": {},
+   "source": [
+    "# Fluid-Structure Interaction in a Flexible Channel\n",
+    "\n",
+    "## Mathematical Model\n",
+    "\n",
+    "Consider the FSI of a flexible channel with fluid flow. The fluid velocity $\\mathbf{v}$ and structural displacement $u$ are coupled through the FSI problem.\n",
+    "\n",
+    "- Structural Equation:\n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\rho_s A_s \\frac{\\partial^2 u}{\\partial t^2} - \\nabla \\cdot \\sigma(u) &= 0 \\quad \\text{in } \\Omega_s \\times (0, T) \\\\\n",
+    "u &= 0 \\quad \\text{on } \\Gamma_{\\text{fixed}} \\times (0, T) \\\\\n",
+    "\\sigma(u) \\cdot \\mathbf{n} &= \\mathbf{t} \\quad \\text{on } \\Gamma_{\\text{interface}} \\times (0, T)\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "\n",
+    "- Fluid Equation:\n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\rho_f \\frac{\\partial \\mathbf{v}}{\\partial t} + \\rho_f (\\mathbf{v} \\cdot \\nabla) \\mathbf{v} - \\nabla \\cdot \\sigma(\\mathbf{v}) &= 0 \\quad \\text{in } \\Omega_f \\times (0, T) \\\\\n",
+    "\\mathbf{v} &= \\mathbf{0} \\quad \\text{on } \\Gamma_{\\text{inlet}} \\times (0, T) \\\\\n",
+    "\\sigma(\\mathbf{v}) \\cdot \\mathbf{n} &= p \\cdot \\mathbf{n} \\quad \\text{on } \\Gamma_{\\text{interface}} \\times (0, T)\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "\n",
+    "- Coupling Conditions:\n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\mathbf{v}(\\mathbf{x}, t) &= \\mathbf{v}_f(\\mathbf{x}, t) \\quad \\text{on } \\Gamma_{\\text{interface}} \\times (0, T) \\\\\n",
+    "\\sigma(u) \\cdot \\mathbf{n} &= \\sigma(\\mathbf{v}) \\cdot \\mathbf{n} \\quad \\text{on } \\Gamma_{\\text{interface}} \\times (0, T)\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "\n",
+    "## Weak Formulation\n",
+    "\n",
+    "Find $u \\in V_s$ and $\\mathbf{v} \\in V_f$ such that\n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\int_{\\Omega_s} \\rho_s A_s \\frac{\\partial^2 u}{\\partial t^2} \\phi_s \\, d\\Omega &- \\int_{\\Omega_s} \\nabla \\cdot \\sigma(u) \\cdot \\nabla \\phi_s \\, d\\Omega = 0 \\\\\n",
+    "\\int_{\\Omega_f} \\rho_f \\frac{\\partial \\mathbf{v}}{\\partial t} \\cdot \\mathbf{\\phi}_f \\, d\\Omega &+ \\int_{\\Omega_f} \\rho_f (\\mathbf{v} \\cdot \\nabla) \\mathbf{v} \\cdot \\mathbf{\\phi}_f \\, d\\Omega - \\int_{\\Omega_f} \\nabla \\cdot \\sigma(\\mathbf{v}) \\cdot \\nabla \\mathbf{\\phi}_f \\, d\\Omega = 0\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "\n",
+    "for all $\\phi_s \\in V_s$ and $\\mathbf{\\phi}_f \\in V_f$.\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f77f76ce",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": ".iga-python",
+   "language": "python",
+   "name": ".iga-python"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

chapter5/compressible_flow_in_a_nozzle.ipynb chapter5/cfd/compressible_flow_in_a_nozzle.ipynb

@@ -0,0 +1,88 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "37cc9bbf",
+   "metadata": {},
+   "source": [
+    "# Flutter Analysis of a Flexible Wing in Fluid Flow\n",
+    "\n",
+    "## Mathematical Model\n",
+    "\n",
+    "Consider the fluid-structure interaction of a flexible wing in a steady airflow. The structural displacement \\(u\\) and fluid velocity \\(\\mathbf{v}\\) are coupled through the FSI problem.\n",
+    "\n",
+    "- Structural Equation:\n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\rho_s A_s \\frac{\\partial^2 u}{\\partial t^2} + c_s \\frac{\\partial u}{\\partial t} - \\nabla \\cdot (\\sigma(u)) &= 0 \\quad \\text{in } \\Omega_s \\times (0, T) \\\\\n",
+    "u &= 0 \\quad \\text{on } \\Gamma_{\\text{fixed}} \\times (0, T) \\\\\n",
+    "\\sigma(u) \\cdot \\mathbf{n} &= p \\cdot \\mathbf{n} \\quad \\text{on } \\Gamma_{\\text{interface}} \\times (0, T)\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "\n",
+    "- Fluid Equation:\n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\rho_f \\frac{\\partial \\mathbf{v}}{\\partial t} + \\rho_f (\\mathbf{v} \\cdot \\nabla) \\mathbf{v} - \\nabla \\cdot \\sigma(\\mathbf{v}) &= 0 \\quad \\text{in } \\Omega_f \\times (0, T) \\\\\n",
+    "\\mathbf{v} &= \\mathbf{0} \\quad \\text{on } \\Gamma_{\\text{inlet}} \\times (0, T) \\\\\n",
+    "\\sigma(\\mathbf{v}) \\cdot \\mathbf{n} &= \\mathbf{t} \\quad \\text{on } \\Gamma_{\\text{wing}} \\times (0, T) \\\\\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "\n",
+    "- Coupling Conditions:\n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\mathbf{v}(\\mathbf{x}, t) &= \\mathbf{v}_f(\\mathbf{x}, t) \\quad \\text{on } \\Gamma_{\\text{interface}} \\times (0, T) \\\\\n",
+    "\\sigma(u) \\cdot \\mathbf{n} &= \\sigma(\\mathbf{v}) \\cdot \\mathbf{n} \\quad \\text{on } \\Gamma_{\\text{interface}} \\times (0, T)\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "\n",
+    "## Weak Formulation\n",
+    "\n",
+    "Find $u \\in V_s$ and $\\mathbf{v} \\in V_f$ such that\n",
+    "\n",
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\int_{\\Omega_s} \\rho_s A_s \\frac{\\partial^2 u}{\\partial t^2} \\phi_s \\, d\\Omega &+ \\int_{\\Omega_s} c_s \\frac{\\partial u}{\\partial t} \\phi_s \\, d\\Omega - \\int_{\\Omega_s} \\nabla \\cdot \\sigma(u) \\cdot \\nabla \\phi_s \\, d\\Omega = 0 \\\\\n",
+    "\\int_{\\Omega_f} \\rho_f \\frac{\\partial \\mathbf{v}}{\\partial t} \\cdot \\mathbf{\\phi}_f \\, d\\Omega &+ \\int_{\\Omega_f} \\rho_f (\\mathbf{v} \\cdot \\nabla) \\mathbf{v} \\cdot \\mathbf{\\phi}_f \\, d\\Omega - \\int_{\\Omega_f} \\nabla \\cdot \\sigma(\\mathbf{v}) \\cdot \\nabla \\mathbf{\\phi}_f \\, d\\Omega = 0\n",
+    "\\end{align*}\n",
+    "$$\n",
+    "\n",
+    "for all $\\phi_s \\in V_s$ and $\\mathbf{\\phi}_f \\in V_f$.\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c4278e28",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": ".iga-python",
+   "language": "python",
+   "name": ".iga-python"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}