Target Corner BC and Finite Width Limiter - Antoinehoff/personal_gkyl_scripts GitHub Wiki

This page documents investigations into target corner boundary conditions (TCBC) for Gkeyll closed-open field line gyrokinetic turbulence simulations and conceptual development of finite width limiter models.

Overview

Current work focuses on addressing numerical instabilities in target corner boundary conditions through alternative TCBC implementations. Additionally, a conceptual finite width limiter model is proposed to address fundamental challenges with zero-width limiter implementations.

Target Corner Boundary Condition (TCBC) Investigation

Alternative TCBC Options Tested

Two alternative TCBCs were explored to improve upon the simple φ = 0 condition:

Option 1: Flux Surface Averaged Potential

Implementation: Set TCBC to flux surface average of potential

φ_{TCBC} = ⟨φ⟩_{fs}

Results:

  • Initial behavior matched expectations
  • Potential at target appeared close to average value
  • Numerical instability developed at t ≈ 40 μs
  • Simulation crash occurred

Option 2: Electron Temperature-Dependent Model

Implementation: Model TCBC as function of electron temperature at target corner

φ_{TCBC} = f(T_{e,target})

Results:

  • Similar initial behavior to Option 1
  • Earlier numerical crash at t ≈ 30 μs
  • Similar instability characteristics

Instability Analysis

Both options resulted in numerical crashes with similar characteristics, suggesting that the instability arises from:

  • Time-dependence of TCBC rather than specific bias applied
  • Rapid oscillations in boundary condition values
  • Coupling between field evolution and boundary updates

Proposed Mitigations

Two potential solutions to reduce time-dependent instabilities:

  1. Reduced Update Frequency

    • Update TCBC less frequently
    • Reduce sensitivity to high-frequency oscillations
    • Maintain quasi-steady boundary conditions

  2. Moving Average Smoothing

    • Apply moving average to TCBC updates
    • Average over past 5, 10, or 15 updates
    • Smooth out rapid fluctuations

Simple φ = 0 Model Success

Despite the challenges with time-dependent TCBCs, the simple model setting φ = 0 at the target has demonstrated:

  • Numerical stability throughout simulation duration
  • Experimental agreement with observed plasma behavior
  • Robust performance across different simulation parameters

This approach serves as the baseline for future finite width limiter development.

Finite-Width Limiter Model (Concept)

Finite Width Limiter Model Conceptual simulation domain for finite width limiter plane. Colored lines on faces represent electrostatic potential boundary values.

The finite width limiter model is meant to address fundamental challenges with zero-width limiter implementations by introducing spatial separation between twist-and-shift boundary conditions and LCFS boundary conditions.

  • Two cells located between inner radial boundary and limiter
  • Decoupled boundaries: TSBC separated from LCFS boundary condition
  • TCBC remains φ = 0 for stability (based on proven success)

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