Update

Author: LukasFuchs

docs/make.jl

@@ -34,6 +34,10 @@ makedocs(
                 "2D" => "man/MomentumTwoD.md", # Checked!
             ],
         ],
+        "Exercises" => Any[
+            "01 - Euler Advection" => "man/exercises/01_Euler_Advection.md",
+            "02 - Heat Diffusion (explicit)" => "man/exercises/02_1D_Heat_explicit.md",
+        ],
         "Examples" => Any[
             "General" => "man/Examples.md",
             "Diffusion Equation" => Any[

docs/src/assets/01_1D_Euler.gif

@@ -79,8 +79,8 @@ This criterion ensures that no particle is advected a greater distance than the
 
 ## Examples
 
-- [2-D advection with constant velocity field](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/AdvectionEquation/2D_Advection.jl)  
-- [Resolution test of 2-D advection](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/AdvectionEquation/2D_Advection_ResolutionTest.jl)
+- [2-D advection with constant velocity field](./examples/Advection2D.md)  
+- [Resolution test of 2-D advection](./examples/AdvectionRestest2D.md)
 
 See the [examples documentation](./Examples.md) for further details.
 

docs/src/man/AdvectMain.md

@@ -48,13 +48,13 @@ Currently, only *Dirichlet* and *Neumann* boundary conditions are supported. Mos
 
 ## Examples
 
-- [1-D oceanic geotherm](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/DiffusionEquation/1D/OceanicGeotherm_1D.jl)  
-- [1-D continental geotherm](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/DiffusionEquation/1D/ContinentalGeotherm_1D.jl)  
-- [Comparison of FD schemes on a Gaussian anomaly](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/DiffusionEquation/1D/Heat_1D_discretization.jl)  
-- [2-D resolution test with Gaussian anomaly](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/DiffusionEquation/2D/Gaussian_Diffusion.jl)  
-- [2-D Poisson equation resolution test](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/DiffusionEquation/2D/Poisson_ResTest.jl)
+- [1-D oceanic geotherm](./examples/OceanicGeotherm.md)  
+- [1-D continental geotherm](./examples/ContinentalGeotherm.md)  
+- [Comparison of FD schemes on a Gaussian anomaly](./examples/GaussianDiffusion1D.md)  
+- [2-D resolution test with Gaussian anomaly](./examples/GaussianDiffusion2D.md)  
+- [2-D Poisson equation resolution test](./examples/PoissonRestest.md)
 
-For explanations, see the [examples documentation](./Examples.md) and the full [example directory](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/DiffusionEquation/).
+For more details, see the full [example directory](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/DiffusionEquation/).
 
 ## Exercises
 
@@ -77,10 +77,9 @@ See the [advection documentation](./AdvectMain.md) and associated source code fo
 
 ## Examples
 
-- [2-D advection with constant velocity field](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/AdvectionEquation/2D_Advection.jl)  
-- [Resolution test of 2-D advection](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/AdvectionEquation/2D_Advection_ResolutionTest.jl)
+- [2-D advection with constant velocity field](./examples/Advection2D.md)  
+- [Resolution test of 2-D advection](./examples/AdvectionRestest2D.md)
 
-See the [examples documentation](./Examples.md) for further details.
 
 ## Exercises
 

docs/src/man/DiffMain.md

@@ -32,7 +32,7 @@ To solve Equation (3) numerically, the spatial domain must be discretized, assig
 
 **Figure 1. 1D Discretization.** Conservative finite difference grid used to solve the 1D diffusive part of the temperature equation. Temperature is defined at centroids, while heat flux is defined at vertices. *Ghost nodes* are introduced to implement *Dirichlet* and *Neumann* boundary conditions.
 
-The example script [Heat_1D_discretization.jl](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/DiffusionEquation/1D/Heat_1D_discretization.jl) demonstrates various numerical schemes for solving the diffusive part of the temperature equation, including *explicit*, *implicit*, *Crank–Nicolson*, and *defect correction* methods. Below, these well-known schemes are briefly described and their respective strengths and limitations highlighted.
+The example script [Heat_1D_discretization.jl](./examples/GaussianDiffusion1D.md) demonstrates various numerical schemes for solving the diffusive part of the temperature equation, including *explicit*, *implicit*, *Crank–Nicolson*, and *defect correction* methods. Below, these well-known schemes are briefly described and their respective strengths and limitations highlighted.
 
 ## Explicit Finite Difference Scheme (FTCS; Forward Euler)
 

docs/src/man/DiffOneD.md

@@ -38,7 +38,7 @@ To numerically solve equation (3), the spatial domain must be discretized and th
 
 **Figure 1. 2D Discretization.** *Conservative finite difference grid* for solving the 2D diffusive temperature equation. Temperature values are defined at the *centroids* (red circles), while heat fluxes are computed at the *vertices* (horizontal flux: blue crosses; vertical flux: green squares). *Ghost nodes* (grey circles) are used to implement *Dirichlet* and *Neumann* boundary conditions.
 
-A detailed implementation of various numerical schemes is provided in the example script [Gaussian_Diffusion.jl](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/DiffusionEquation/2D/Gaussian_Diffusion.jl). This example demonstrates the application of several methods for solving the diffusive part of the 2D temperature equation:
+A detailed implementation of various numerical schemes is provided in the example script [Gaussian_Diffusion.jl](./examples/GaussianDiffusion2D.md). This example demonstrates the application of several methods for solving the diffusive part of the 2D temperature equation:
 
 - **Explicit scheme**
 - **Fully implicit scheme**

docs/src/man/DiffTwoD.md

@@ -244,7 +244,7 @@ The input parameters are:
 
 For more details please refer to the [source code](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/src/Tracers/2Dsolvers.jl).
 
->**Note:** Currently, temperature is not intended to be advected via tracers, as this would require the update of the tracer temperature via incremental changes rather than absolute value. Within the [2-D advection example](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/AdvectionEquation/2D_Advection.jl) temperature advection is only used assuming non-diffusive process. Thus, no update of the tracer temperature is required! 
+>**Note:** Currently, temperature is not intended to be advected via tracers, as this would require the update of the tracer temperature via incremental changes rather than absolute value. Within the [2-D advection example](./examples/Advection2D.md) temperature advection is only used assuming non-diffusive process. Thus, no update of the tracer temperature is required! 
 
 The advection of temperature and the update of the temperature field on the centroids is called, for example, like [here](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/AdvectionEquation/2D_Advection.jl): 
 

docs/src/man/Ini.md

@@ -85,18 +85,17 @@ Together, the momentum and continuity equations allow solving for $v_x$, $v_y$,
 
 The following examples demonstrate the application of the Stokes equations:
 
-- [1D channel flow with constant and depth-dependent viscosity](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/StokesEquation/1D/ChannelFlow_1D.jl)  
-- [2D falling block benchmark](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/StokesEquation/2D/FallingBlockBenchmark.jl)  
-- [2D falling block with constant viscosity (defect correction)](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/StokesEquation/2D/FallingBlockConstEta_DC.jl)  
-- [2D falling block with variable viscosity (defect correction)](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/StokesEquation/2D/FallingBlockVarEta_DC.jl)  
-- [2D viscous inclusion problem](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/StokesEquation/2D/ViscousInclusion.jl)  
-- [2D Rayleigh–Taylor instability benchmark](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/StokesEquation/2D/RTI.jl)
+- [1D channel flow with constant and depth-dependent viscosity](./examples/ChannelFlow1D.md)  
+- [2D falling block benchmark](./examples/FallingBlockBenchmark.md)  
+- [2D falling block with constant viscosity (defect correction)](./examples/FallingBlockDC.md)  
+- [2D falling block with variable viscosity (defect correction)](./examples/FallingBlockDC.md)  
+- [2D viscous inclusion problem](./examples/ViscousInclusion.md)  
+- [2D Rayleigh–Taylor instability benchmark](./examples/RTI_growth_rate.md)
 
 Examples of coupled temperature–momentum systems (i.e., **convection models**) using **operator splitting** include:
 
-- [Mixed heated convection models](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/examples/MixedHeatedConvection/)
+- [Mixed heated convection models](./examples/MixedHeatedConvection.md)
 
-See the [examples documentation](./Examples.md) for further details.
 
 ## Exercises
 

docs/src/man/MomentumMain.md

@@ -0,0 +1,7 @@
+# [01 - Euler Advection(1D)](https://github.com/GeoSci-FFM/GeoModBox.jl/blob/main/exercises/01_1D_Euler_Advection.ipynb)
+
+This exercise focuses on starting programming with `Julia` and discretizing and solving a partial differential equation. 
+
+![Exercise1a](../../assets/01_1D_Euler.gif)
+
+**Figure 1. 1-D Particle Advection.**