Documentation clarification (#625)

Author: wilfonba

docs/documentation/case.md

@@ -182,7 +182,7 @@ The code outputs error messages when an empty region is left in the domain.
 Some parameters, as described above, can be defined by analytical functions in the input file. For example, one can define the following patch:
 
 ```shell
-'patch_icpp(2)%geometry'    : 15,
+'patch_icpp(2)%geometry'    : 1,
 'patch_icpp(2)%x_centroid'  : 0.25,
 'patch_icpp(2)%length_x'    : 9.5,
 'patch_icpp(2)%vel(1)'      : 0.,
@@ -228,7 +228,7 @@ For example, to add a 2D Hardcoded patch with an id of 200, one would add the fo
 
 and use `patch_icpp(i)%%geometry = 7` and `patch_icpp(i)%%hcid = 200` in the input file.
 Additional variables can be declared in `Hardcoded1[2,3]DVariables` and used in `hardcoded1[2,3]D`.
-As a convention, any hard coded patches that are part of the MFC master branch should be identified as 1[2,3]xx where the first digit indites the number of dimensions.
+As a convention, any hard coded patches that are part of the MFC master branch should be identified as 1[2,3]xx where the first digit indicates the number of dimensions.
 
 #### Parameter Descriptions
 
@@ -353,9 +353,9 @@ Details of implementation of viscosity in MFC can be found in [Coralic (2015)](r
 | `mp_weno`              | Logical | Monotonicity preserving WENO |
 | `riemann_solver`       | Integer | Riemann solver algorithm: [1] HLL*; [2] HLLC; [3] Exact*	 |
 | `low_Mach`             | Integer | Low Mach number correction for HLLC Riemann solver: [0] None; [1] Pressure (Chen et al. 2022); [2] Velocity (Thornber et al. 2008)	 |
-| `avg_state`	         | Integer | Averaged state evaluation method: [1] Roe averagen*; [2] Arithmetic mean  |
+| `avg_state`	         | Integer | Averaged state evaluation method: [1] Roe average*; [2] Arithmetic mean  |
 | `wave_speeds`          | Integer | Wave-speed estimation: [1] Direct (Batten et al. 1997); [2] Pressure-velocity* (Toro 1999)	 |
-| `weno_Re_flux`         | Logical | Compute velocity gradient using scaler divergence theorem	 |
+| `weno_Re_flux`         | Logical | Compute velocity gradient using scalar divergence theorem	 |
 | `weno_avg`          	 | Logical | Arithmetic mean of left and right, WENO-reconstructed, cell-boundary values |
 | `dt`                   | Real    | Time step size |
 | `t_step_start`         | Integer | Simulation starting time step |
@@ -434,7 +434,7 @@ Practically, `weno_eps` $<10^{-6}$ is used.
 - `wave_speeds` specifies the choice of the method to compute the left, right, and middle wave speeds in the Riemann solver by an integer of 1 and 2.
 `wave_speeds = 1` and `2` correspond to the direct method ([Batten et al., 1997](references.md#Batten97)), and indirect method that approximates the pressures and velocity ([Toro, 2013](references.md#Toro13)), respectively.
 
-- `weno_Re_flux` activates the scaler divergence theorem in computing the velocity gradients using WENO-reconstructed cell boundary values.
+- `weno_Re_flux` activates the scalar divergence theorem in computing the velocity gradients using WENO-reconstructed cell boundary values.
 If this option is false, velocity gradient is computed using finite difference scheme of order 2 which is independent of the WENO order.
 
 - `weno_avg` it activates the arithmetic average of the left and right, WENO-reconstructed, cell-boundary values.
@@ -592,7 +592,7 @@ Details of the transducer acoustic source model can be found in [Maeda and Colon
 
 - `%%element_on` specifies the element number of the transducer array that is on. The element number starts from 1. If all elements are on, set `%%element_on` to 0.
 
-- `%%element_spacing_angle` specifies the spacing angle between adjacent transducer in radian. The total aperture (`%%aperture`) is set, so each transducer element is smaller if `%%element_spacing_angle` is larger.
+- `%%element_spacing_angle` specifies the spacing angle between adjacent transducer in radians. The total aperture (`%%aperture`) is set, so each transducer element is smaller if `%%element_spacing_angle` is larger.
 
 - `%%element_polygon_ratio` specifies the ratio of the polygon side length to the aperture diameter of each transducer element in a circular 3D transducer array. The polygon side length is calculated by using the total aperture (`%%aperture`) as the circumcicle diameter, and `%%num_elements` as the number of sides of the polygon. The ratio is used specify the aperture size of each transducer element in the array, as a ratio of the total aperture. 
 
@@ -678,7 +678,7 @@ Implementation of the parameters into the model follow [Ando (2010)](references.
 
 | Parameter              | Type    | Description |
 | ---:                   | :----:  | :--- |
-| `perturb_flow`         | Logical | Perturb the initlal velocity field by random noise |
+| `perturb_flow`         | Logical | Perturb the initlial velocity field by random noise |
 | `perturb_flow_fluid`   | Integer | Fluid density whose flow is to be perturbed |
 | `perturb_flow_mag`     | Real    | Set the magnitude of flow perturbations |
 | `perturb_sph`          | Logical | Perturb the initial partial density by random noise |
@@ -789,15 +789,15 @@ The entries labeled "Characteristic." are characteristic boundary conditions bas
 | 4    | Sweep line 		| 2     | Y      | Not coordinate aligned. Requires `[x,y]_centroid` and `normal(i)`. |
 | 5    | Ellipse 		    | 2     | Y      | Requires `[x,y]_centroid` and `radii(i)`. |
 | 6    | N/A 		        | 2     | N      | No longer exists. Empty. |
-| 7    | 2D analytical 	    | 2     | N      | Assigns the primitive variables as analytical functions. |
+| 7    | 2D Hardcoded 	    | 2     | N      | Assigns the primitive variables as analytical functions. |
 | 8    | Sphere 		    | 3     | Y      | Requires `[x,y,z]_centroid` and `radius` |
 | 9    | Cuboid 		    | 3     | N      | Coordinate-aligned. Requires `[x,y,z]_centroid` and `length_[x,y,z]`. |
 | 10   | Cylinder 		    | 3     | Y      | Requires `[x,y,z]_centroid`, `radius`, and `length_[x,y,z]`. |
 | 11   | Sweep plane 	    | 3     | Y      | Not coordinate-aligned. Requires `x[y,z]_centroid` and `normal(i)`. |
 | 12   | Ellipsoid 		    | 3     | Y      | Requires `[x,y,z]_centroid` and `radii(i)`. |
-| 13   | 3D analytical 	    | 3     | N      | Assigns the primitive variables as analytical functions |
+| 13   | 3D Hardcoded 	    | 3     | N      | Assigns the primitive variables as analytical functions |
 | 14   | Spherical Harmonic | 3     | N      | Requires `[x,y,z]_centroid`, `radius`, `epsilon`, `beta` |
-| 15   | 1D analytical      | 1     | N      | Assigns the primitive variables as analytical functions  |
+| 15   | 1D Hardcoded      | 1     | N      | Assigns the primitive variables as analytical functions  |
 | 16   | 1D bubble pulse    | 1     | N      | Requires `x_centroid`, `length_x` |
 | 17   | Spiral             | 2     | N      | Requires `[x,y]_centroid` |
 | 18   | 2D Varcircle       | 2     | Y      | Requires `[x,y]_centroid`, `radius`, and `thickness` |