parallel-2D-advection

A 2D advection program which advects a Gaussian u(x,y) at a fixed velocity

Content

• How To Run?
  • Requirements
  • WARNING!
• Scenario
• Plots
• Development
  • Parallel Implementation
  • Configuration Modification for Realism
  • Adding Vertical Shear
  • Calculating Vertically Averaged Distribution

How To Run?

In a terminal...

• Navigate to the parallel-2D-advection directory
• Use the command bash build.sh
  • If a permission error is given, use the command chmod +x and try again
• Wait for the terminal to report the process was successful
• Check the out directory for the .png files generated by gnuplot
  • Alternatively checkout the plots directory to see a history of the 2D advection plots as the program was improved

Requirements

• OpenMP
• gcc
• gnuplot

WARNING!

• GCC 9 or older implements the changes made to default(none) in OpenMP 4.0
  • default(none) NO LONGER predetermines "const variables with no mutable members" as shared (breaking backwards compatibility)
  • To implement a program which compiles for any GCC version, any const variables will be declared as firstprivate
• Read more about the issue here

Purpose

The closest atmosphere to the Earth's surface is called the "Atmospheric Boundary Layer", and at this level the wind speed increases with height.
For example material emitted from a chimmey is advected at different horizontal speeds depending on its height.

• Read more about:
  • Atmospheric Boundary Layer
  • Wind-Log-Profiles

parallel-2D-advection implements its own version of a numerical solution to calculate the advection equation, thus simulating the movement of a cloud of material in the atmospheric boundary layer.

Plots

The final plots for the 2D advection with all modifications implemented. (all stages can be found in the plots directory)

Initial	Final	Vertically Averaged Distribution

Development

Several changes were made to the program over its development.

Parallel Implementation

Ten loops were present in the initial program however not all could be implemented with parallel execution. (Loops are labeled within the code)

No.	Parallel Implementation Status
1	Successful
2	Successful
3	Successful
4	Failed: Writing to a singular file using multiple threads breaks output dependency. Each thread overwrites the other threads changes
5	Failed: Each iteration of the outer loop depends upon the updates made by the previous. Flow dependency is broken in parallel as the time steps become unordered
6	Successful
7	Successful
8	Successful
9	Successful
10	Failed: same case as LOOP 4
11	Failed: same case as LOOP 4

Configuration Modification for Realism

The initial calculation was not particularly realistic. Several configuration modifications were made to improve the realism.

Variable	Initial	Improved
MAX_X	1.0	30.0
MAX_Y	1.0	30.0
CENTER_X	0.1	3.0
CENTER_Y	0.1	15.0
SIGMA_X	0.03	1.0
SIGMA_Y	0.03	5.0
N_STEPS	1500	800
VEL_X	0.01	1.0
VEL_Y	0.01	0.0

Adding Vertical Shear

To simulate a realistic advection, modifications are implimented so the horizontal velocity varies with height.
NB: Added (A) / Modified (M)

A/M	Name	Desc
A	calc_vel_x()	Calculates the horizontal velocity using a logarithmic profile (adds vertical shear)
A	F_VEL	Friction velocity (meters per second)
A	R_LEN	Roughness length
A	VK_CONST	Von Karman's constant
M	VEL_X	Calls 'calc_vel_x()' instead of using a literal value
M	Loop 8	Horizontal velocity is calculated using 'calc_vel_x()' instead of a constant

Calculating Vertically Averaged Distribution

To understand the advection better, an additional plot is created for the horizontal profile of advected material see Plots

• vavg_u was added: Stores vertical averages for u_val[x,y] (calloc: init indexes as 0)
• Loop 9 was modifed: inner loop sums the u values (y), outer loop divides the sum by total points of y to get vertical average
  • Once the loop completes vavg_u conntains the vertically averaged distribution of u[x,y]
• Loop 11 was added: prints values of vavg_u to v_averaged.dat which is used by v_averaged.gnuplot to create the additional plot