add more English exercises

docs/make.jl

@@ -40,13 +40,13 @@ makedocs(
             "02 - 1D Heat Diffusion (explicit)" => "man/exercises/02_1D_Heat_explicit.md", # Checked! 
             "03 - 1D Heat Diffusion (implicit)" => "man/exercises/03_1D_Heat_implicit.md", # Checked!
             "04 - 2D Heat Diffusion (stationary)" => "man/exercises/04_2D_Diffusion_Stationary.md", # Checked!
-            "05 - 2D Heat Diffusion (Plume)" => "man/exercises/05_2D_Diffusion_TD_Plume.md", # Checked! 
-            "05 - 2D Heat Diffusion (Sill)" => "man/exercises/05_2D_Diffusion_TD_Sill.md", # Checked!
+            "05a - 2D Heat Diffusion (Plume)" => "man/exercises/05_2D_Diffusion_TD_Plume.md", # Checked! 
+            "05b - 2D Heat Diffusion (Sill)" => "man/exercises/05_2D_Diffusion_TD_Sill.md", # Checked!
             "06 - 1D Advection" => "man/exercises/06_1D_Advection.md", # Checked!
             "07 - 2D Energy Conservation" => "man/exercises/07_2D_Energy_Equation.md", # Checked!
             "08 - 1D Stokes" => "man/exercises/08_1D_Stokes.md",
-            # "09 - 2D Falling Block (steady state)" => "man/exercises/09_2D_Falling_Block.md",
-            # "10 - 2D Falling Block (time-dep)" => "man/exercises/10_2D_Falling_Block_td.md",
+            "09 - 2D Falling Block (steady state)" => "man/exercises/09_2D_Falling_Block.md",
+            "10 - 2D Falling Block (time-dep)" => "man/exercises/10_2D_Falling_Block_td.md",
             # "11 - 2D Thermal Convection" => "man/exercises/11_2D_Thermal_Convection.md",
             # "12 - 2D Thermal Convection (scaled)" => "man/exercises/12_2D_Thermal_Convection_scaled.md",
             # "13 - Blankenbach Benchmark" => "man/exercises/12_Blankenbach_Benchmark.md",

docs/src/man/Exercises.md

@@ -29,3 +29,14 @@ All exercises were performed on a single CPU: *AMD Ryzen 7 7735U with Radeon Gra
 | --------------- | ---------------------------------- | ----------------- |
 | 1               | Euler Advection                    | 5.741             |
 | 2               | 1-D Heat Diffusion <br/> (explicit) | 1) 9.342 (1.14) <br/> 2) 9.975 (1.087) <br/> 3) 9.616 (1.017) |
+| 3               | 1-D Heat Diffusion <br/> (implicit) | 1) 12.641 (1.749) <br/> 2) 13.537 (1.720) <br/> 3) 12.157 (1.731) | 
+| 4               | 2-D Steady State Heat Equation     | 13.471 (2.069) |
+| 5a              | 2-D Time-dep. Heat Equation (Plume) | 1) Explicit: 18.632 (4.799) <br/> 2) Implicit: 78.201 (60.828) |
+| 5b              | 2-D Time-dep. Heat Equation (Sill)  | 1) Explicit: 17.856 (4.566) <br/> 2) Implicit: 39.626 (22.679) |
+| 6               | 1-D Advection Scheme                | 1) FTCS: 11.644 (4.019) <br/> 2) Upwind: 11.03 (4.042) <br/> 3) Downwind: 11.465 (3.343) <br/> 4) LAX: 11.272 (3.405) <br/> 5) SLF: 11.312 (3.48) <br/> 6) Semilag: 14.318 (3.604) <br/> 7) Tracers: 15.662 (4.944) |
+| 7               | 2-D Energy Equation                 | 1) Upwind+explicit: 17.468 (2.979) <br/> 2) Upwind+implicit: 31.441 (10.842) <br/> 3) Upwind+CNA: 32.065 (12.222) <br/> 4) Upwind+ADI: 121.665 (99.807) <br/> 5) Upwind+dc: 30.45 (11.401) <br/> 6) SLF+explicit: 22.002 (2.872) <br/> 7) SLF+implicit: 28.751 (8.911) <br/> 8) SLF+CNA: 29.876 (9.28) <br/> 9) SLF+ADI: 120.018 (98.74) <br/> 10) SLF+dc: 28.179 (9.379) <br/> 11) SL+explicit: 22.969 (6.334) <br/> 12) SL+implicit: 30.634 (9.682) <br/> 13) SL+CNA: 32.415 (11.566) <br/> 14) SL+ADI: 133.871 (110.704) <br/> 15) SL+dc: 35.364 (12.301) <br/> 16) Tracers+explicit: 89.499 (65.913) <br/> 17) Tracers+implicit: 108.464 (84.209) <br/> 18) Tracers+CNA: 112.171 (89.219) <br/> 19) Tracers+ADI: 186.71 (161.611) <br/> 20) Tracers+dc: 115.737 (89.089) |
+| 8               | 1-D Stokes Equation                 | 8.489 (0.212) |
+| 9               | 2-D Falling Block (steady state)    | 20.764 (0.891) | 
+| 10              | 2-D Falling Block (time-dep.)       | 1) Upwind: 33.295 (3.68) <br/> 2) SLF: 32.333 (3.629) <br/> 3) SL: 37.537 (3.755) <br/> 4) Tracers: 36.291 (6.12) |
+
+

docs/src/man/exercises/09_2D_Falling_Block.md

@@ -0,0 +1,14 @@
+# [09 – Falling Block](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/exercises/09_2D_Falling_Block_en.ipynb)
+
+In this exercise, students simulate the motion of a dense block sinking in a viscous fluid under the influence of gravity. The problem is set up in two dimensions with constant viscosity (*isoviscous* case) and *free-slip* velocity boundary conditions on all sides.  
+
+The goals of this exercise are to:  
+- Set up the **2-D model geometry** and define the block phase within the background medium.  
+- Assign appropriate **physical parameters**, such as viscosity, density contrast, and gravity.  
+- Implement the **momentum and mass conservation equations** using the finite difference method.  
+- Assemble and solve the resulting **linear system of equations** for velocities and pressure.  
+- Visualize the **velocity field** and the interaction between the sinking block and the surrounding viscous medium.  
+
+This exercise provides a simple but powerful benchmark problem to validate the Stokes solver and to understand the dynamics of density-driven flow in an isoviscous medium.  
+
+![Exercise09](../../assets/09_FallingBlock_Instantan.png)

docs/src/man/exercises/10_2D_Falling_Block_td.md

@@ -0,0 +1,22 @@
+# [10 – 2D Falling Block (time-dependent)](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/exercises/10_2D_Falling_Block_td_en.ipynb)
+
+This exercise extends the **falling block problem** to a **time-dependent** case with constant viscosity.  
+The problem couples the solution of the **momentum conservation equation** (Stokes system) with the **advection equation**, where density (or phase) is transported through the velocity field.  
+
+The main objectives are:  
+
+1. Setting up the model domain with a dense block embedded in a viscous medium under gravity,  
+2. Defining **free-slip** velocity boundary conditions on all sides,  
+3. Assembling the coefficient matrix for the Stokes system (constant viscosity → assembled once),  
+4. Implementing a **time loop** that in each step:  
+   - Updates the right-hand side with the current density distribution,  
+   - Solves the Stokes system for velocity and pressure,  
+   - Advects density (or phase) using different numerical schemes, including tracers,  
+   - Recomputes the time step and visualizes the solution,  
+5. Producing an animation of the sinking block over time.  
+
+This problem demonstrates how to couple **Stokes flow** with **advection of material properties**, and how the choice of advection scheme affects the evolution of the solution.  
+
+![Exercise10](../../assets/10_Falling_block_iso_td_tracers.gif)
+
+**Figure 1.** Time evolution of the sinking block in a viscous medium using the tracer advection method.