Parsedfunction for triangular (or sawtooth) waveform

[adhoc00]

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Question

Hello,
I am using the ParsedFunction to compute a triangular (or sawtooth) wave function for my boundary condition, as shown in the attached figure. However, the waveform obtained from the postprocessor output differs from the expected result.
Please advise on what might be causing this discrepancy? Thanks.

For reference, I have included the ParsedFunction definition along with the corresponding postprocessor output below.

[Functions]
  [pressure_cycle]
    type = ParsedFunction
    value = '
      if(t < 0.5, P_min + 2*(P_max - P_min)*t,
      if(t < 1.0, P_max - 2*(P_max - P_min)*(t - 0.5),

      if(t < 1.5, P_min + 2*(P_max - P_min)*(t - 1.0),
      if(t < 2.0, P_max - 2*(P_max - P_min)*(t - 1.5),

      if(t < 2.5, P_min + 2*(P_max - P_min)*(t - 2.0),
      if(t < 3.0, P_max - 2*(P_max - P_min)*(t - 2.5),

      P_min ))))))
    '
    vars = 'P_min P_max'
    vals = '6.0   15.0'
  []
    [pressure_function]
    type = ParsedFunction
    # Triangular wave function with:
    # - Amplitude: ±4 MPa (from baseline of 8 MPa to peaks at 6 and 14 MPa)
    # - Period: 1.0 cycle
    # - Baseline: 8 MPa
    # - Linear ramping
    value = '8 + 4 * (1 - 4 * abs(t - floor(t + 0.5)))'
    # Alternative formulation with explicit min/max:
    # value = '8 + 4 * (2 * (t - floor(t)) - 1) * (1 - 2 * min(t - floor(t), floor(t + 1) - t))'
    
    # For a more explicit version that matches the image exactly:
    # value = 'if(t - floor(t) < 0.5,
    #                8 + 4 * 2 * (t - floor(t)),        # Rising phase
    #                8 + 4 * (1 - 2 * (t - floor(t))))' # Falling phase
  []
[]

 [Postprocessors]
  [avg]
    type = FunctionValuePostprocessor
    function = pressure_function
    outputs = csv
  []
[]

[lindsayad]

I'm confused. You pasted two different ParsedFunctions. The Postprocessor uses pressure_function. What is pressure_cycle for? Also if you could say exactly what is used to create the two lines (e.g. what does Pressure correspond to, what does $\sigma_1 - \sigma_3$ correspond to), that would be great

[adhoc00]

Hi @lindsayad both pressure_function and pressure_cycle ParsedFunctions are my attempt to compute the triangular wave function. I should have named pressure_cycle as pressure_function_alternative. I tried both, and they gave different outputs compared to what is in the image. Please ignore the \sigma_1 - \sigma_3 (deviatoric stress). It is an alternative BC that I can use in my simulation if I prefer. My goal is the pressure BC. Basically, I'm simulating a cyclic pressure at the boundary of a salt cavern. Pressure injection rises linearly and spans 0 to 0.5 cycles, while pressure extraction decreases linearly and spans 0.5 to 1.0 cycles. Then the cycle repeats. In this case, the period is 1 cycle.

[lindsayad]

Thanks for more detail. However, if I'm ignoring $\sigma_1 - \sigma_3$, then all that's left is the Pressure plot. It would be helpful to know exactly what's wrong about it. I can see that the Pressure is clearly offset in phase from $\sigma_1 - \sigma_3$, so if Pressure was supposed to match that, then it's clear what's wrong

[adhoc00]

Hello @lindsayad I found the solution to this problem using the PeriodicFunction in the MOOSE function type. I can customize any function as a base_function and feed it to this PeriodicFunction.

[lindsayad]

Great!