Hybrid Adaptive Multiresolution for Reactive Flows
Overview
Simulating reactive flows with shocks, flames, and detonations requires resolving thin reaction zones embedded in much larger computational domains. Traditional block-structured adaptive mesh refinement (AMR) excels at focusing resolution where needed, but refinement criteria based on local solution features can be unreliable for stiff reactive systems.
This work introduces HAMR (Hybrid Adaptive Multiresolution), which combines the geometric flexibility of block-structured AMR with the rigorous error control of multiresolution (MR) analysis. The result is a method that automatically identifies regions requiring high resolution while enabling aggressive coarsening elsewhere—achieving significant computational savings without sacrificing accuracy.
Adaptive Mesh Visualization
The video below demonstrates HAMR applied to the Hawley-Zabusky problem, showing how the adaptive mesh tracks complex shock interactions and instabilities in real time. Notice how refinement follows the evolving flow structures while maintaining efficiency in smooth regions.
Hawley-Zabusky problem simulated with HAMR: a shock impinging on an oblique material interface. The adaptive mesh (shown overlaid) dynamically tracks shock fronts, contact discontinuities, and developing baroclinic vorticity generation while coarsening in smooth regions.
Key Innovations
MR Smoothness Indicators
Wavelet-based multiresolution analysis provides mathematically rigorous smoothness indicators that reliably detect features requiring refinement, even for stiff reactive systems where gradient-based criteria fail.
Solver-Adaptive Methods
In regions identified as smooth by MR analysis, expensive flux calculations are replaced with high-order interpolation from coarser data—reducing computational cost while maintaining accuracy within prescribed tolerances.
Block-Structured Flexibility
Retains the parallelization advantages and geometric flexibility of block-structured AMR, enabling efficient implementation on modern HPC architectures with established AMR frameworks.
The Challenge
Reactive flow simulations face a fundamental efficiency problem: reaction zones are extremely thin (often just a few grid cells), but accurately capturing their dynamics requires resolving them at all times throughout a much larger domain. Standard AMR addresses this by refining only near important features, but the refinement criteria themselves pose challenges:
- Gradient-based criteria can miss incipient features or trigger unnecessary refinement in non-critical regions
- Physics-based criteria require problem-specific tuning and may not generalize across flow regimes
- Conservative approaches over-refine to ensure safety, negating much of AMR's efficiency benefit
Multiresolution analysis provides a solution by quantifying the local truncation error directly from the solution data, enabling refinement decisions with rigorous error bounds.
Validation Problems
HAMR was validated on a series of increasingly complex test problems:
- Interacting Blast Waves: Classic 1D test with colliding shocks demonstrating shock-capturing accuracy under mesh adaptation
- Hawley-Zabusky Problem: 2D shock impinging on an oblique material interface with baroclinic vorticity generation, testing adaptation to evolving multiscale structures
- Cellular Detonation: Reactive flow with cellular instabilities, validating the method for stiff chemistry and thin reaction zones
- Reactive Turbulence: 3D turbulent combustion demonstrating scalability and efficiency for production-scale simulations
Performance
Compared to uniform-grid simulations at equivalent effective resolution, HAMR achieves substantial speedups while maintaining solution accuracy within prescribed error tolerances. The combination of aggressive mesh coarsening in smooth regions with solver-adaptive flux calculations yields multiplicative efficiency gains.
The method integrates with existing block-structured AMR frameworks, enabling adoption in production simulation codes without fundamental architectural changes.
Publication
B. Gusto and T. Plewa. "A hybrid adaptive multiresolution approach for the efficient simulation of reactive flows." Computer Physics Communications.