Update requirements based on comments and discussion

components/omega/doc/design/MeshClass.md

@@ -1,39 +1,56 @@
-(omega-design-mesh)=
+(omega-design-horz-mesh)=
 # Mesh 
 
 ## 1 Overview
 
-The mesh class will contain the YAKL arrays which describe the mesh and are used in the computation of the tendency terms in the discrete governing equations.
+The mesh class will contain the YAKL arrays which describe the horizontal mesh and are used in the computation of the tendency terms in the discrete governing equations. OMEGA will separate the horizontal mesh variables from the vertical mesh information.
 
 ## 2 Requirements
 
-### 2.1 Requirement: OMEGA will use the previously estabilished MPAS Mesh Spec
+### 2.1 Requirement: OMEGA will use the previously established MPAS Mesh Spec
 
-The OMEGA mesh information should be compatiable with the [MPAS Mesh Specification](https://mpas-dev.github.io/files/documents/MPAS-MeshSpec.pdf).
+The OMEGA mesh information should be compatible with the [MPAS Mesh Specification](https://mpas-dev.github.io/files/documents/MPAS-MeshSpec.pdf).
 
-### 2.2 Requirement: Functionality is needed to read the mesh on the host and transfer relevant data to the device for comutation
+### 2.2 Requirement: Functionality is needed to read the mesh on the host and transfer relevant data to the device for computation
 
 Not all mesh information is required in computing the tendency terms on the device, e.g. lonCell, latCell, etc. 
-However, other arrays will need to allocated and copied to the device for use in tendency computation.
-One option is to template the mesh class so a mesh object can be created for both the host and device, with a method to perform the copy between the two object types.
+However, other arrays will need to be allocated and copied to the device for use in tendency computation.
+The mesh class will explicitly include host and device YAKL arrays for each variable.
+A class method will be included to copy the relevant mesh information to the device.
 
 ### 2.3 Requirement: Zero-based cell, edge, and vertex numbering
 
-Although the existing MPAS Mesh spec uses a one-based mesh numbering, zero-based mesh numbering is required to be compatiable with the zero-based indexing used for YAKL arrays.
+Although the existing MPAS Mesh spec uses a one-based mesh numbering, zero-based mesh numbering is required to be compatible with the zero-based indexing used for YAKL arrays.
 
 ### 2.4 Requirement: Work with Decomp class to decompose mesh
 
+The mesh class will reference the partitioned connectivity arrays created by the Decomp class.
 
-### 2.5 Desired: Ability to support multiple independent mesh objects
+### 2.5 Requirement: Mesh variables will be associated with metadata to describe data 
 
-This flexibility is required to support future implmentations of spatially split barotropic and baroclinic modes that are computed on different resolution 
+Following the Metadata and IO designs, the YAKL arrays for the mesh variables will be associated with information about the represented values.
 
-### 2.6 Desired: OMEGA can read in a reduced number of mesh variables and compute the remaning array information online.
+### 2.6 Requirement: I/O to obtain mesh data
+
+The Mesh class will have a method to read in the mesh information not obtained by the Decomp class. 
+
+### 2.7 Desired: Ability to support multiple independent mesh objects
+
+This flexibility is required to support future implementations of spatially split barotropic and baroclinic modes that are computed on different resolution meshes.
+Additionally, this flexibility can be used to support separate domain decompositions for the barotropic and baroclinic meshes, which can help optimize the communication frequency for the barotropic subcycling via wide barotropic halos.
+
+### 2.8 Desired: OMEGA can read in a reduced number of mesh variables and compute the remaining array information online.
 
 Many of the mesh variables are not independent, e.g.  areaCell, weightsOnEdge, etc., and can be computed from a reduced set of mesh variables.
-This functionality could be used to reduce mesh/restart file size for high resoultion meshes.  
-Builiding in this flexibility would allow for all mesh-related calculations to be availiable within the code base instead of spreading them amonst various utility programs in MPAS-Tools.
-The functions used to compute the dependent mesh information can also be used to verify mesh information provided in the mesh input stream.
+This functionality could be used to reduce mesh/restart file size for high resolution meshes.  
+Building in this flexibility would allow for all mesh-related calculations to be available within the code base instead of spreading them amongst various utility programs in MPAS-Tools.
+This will improve the ability to maintain and unit test the mesh calculations in MPAS-Tools.
+The functions used to compute the dependent mesh information can also be used to verify any mesh information that is provided in the mesh input stream.
+
+As standard practice, all necessary internally computed mesh information will be output in a single file for post-processing purposes.
+A checksumming strategy will be implemented to avoid situations where simulation data and mesh information are mismatched during post processing. 
+
+Where appropriate, some additional derived quantities (e.g. reciprocals) will also be included to improve the performance of device-side calculations.
 
 ## 3 Algorithmic Formulation