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Support Adams-Bashforth time integration in checkpoint #174

@ia267

Description

@ia267

Current ADIOS2 checkpoint implementation only properly handles Runge-Kutta time integration methods. Adams-Bashforth methods (AB2-AB4) requires saving additional state information (previous derivatives) to properly restart simulations.

Implementation details:

  • Extend checkpoint_io.f90 to identify when Adams-Bashforth methods are used
  • Add support for storing previous derivatives (or flow field) in a olds array
  • Preserve the time stepper counter (iter) during checkpoint/restart
  • Handle proper AB startup sequence after restarts

Acceptance criteria:

  • Simulation can be properly checkpointed and restarted with AB2, AB3 and AB4 time integration methods
  • Numerical results before and after are identical (within floating point tolerance)
  • No performance degradation for non-AB methods

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