Positive Preserving Scheme

[Zhengyu-Huang]

Describe the bug

In our simulation, to remain positiveness for the tracer, we have

• vertical upwind scheme
• horizontal limiter (require SSP time stepper)

To Reproduce

We have the following issues

• We still have negative tracer values
• The maximum dt for SSP time stepper and the vertical upwind scheme is small

Debug strategies

• test other SSP schemes (i.e., SSP332) (see Test SSP332 #1691 )
• Single-column upwinding tests using 1D EDMFX test setup (see Single-column upwinding tests using 1D EDMFX test setup #1772 )
• try explicit treatment of the tracer variables (passive tracer)
• test positive pressing for horizontal limiter (advection equation)
  • @dennisYatunin and @valeriabarra both tested it and reproduced the original results from the paper. You can see the report here. You can see that with high enough horizontal resolution, h_elem 20, with SSP333, we reach undershoots that are only of the order of 1.5802e-13
• use exact Jacobian for Zalesak
  • this can be done only after the Implicit Solver interface update is complete (CC SDI Implicit Solver Interface Updates ClimaCore.jl#1230)

[Zhengyu-Huang]

It is weird that 1) we still have negative value for first order upwind scheme 2) central difference is better than first order upwind scheme

[valeriabarra]

It is weird that 1) we still have negative value for first order upwind scheme 2) central difference is better than first order upwind scheme

Since at the meeting they said that this test was not relevant for testing upwinding, I will remove the comment for clarity

[szy21]

Superseded by ClimaCore Issue: CliMA/ClimaCore.jl#1327