Evaluation of Adaptive Mesh Refinement in Capturing Shocks and Vortices in Compressible Flow

In multiscale simulations of compressible flow, there is often a tradeoff between coarse discretizations that reduce computational cost and fine meshes required to resolve critical physics. High resolution is typically necessary to capture sharp gradients and nonlinear features such as shocks, detonation fronts, and vortex dynamics. However, uniform mesh refinement across the entire domain is often computationally prohibitive. Adaptive Mesh Refinement (AMR) offers a promising alternative by dynamically concentrating resolution in regions of interest. Despite its potential, the effectiveness of AMR in capturing strongly nonlinear and transient phenomena—such as shock formation, detonation propagation, and vortex generation—remains an open question.

This work evaluates the fidelity and efficiency of AMR in resolving such features by simulating canonical and experimental shock-dominated flows using both Euler and Navier–Stokes formulations. Shocks are treated as steep gradients or discontinuities, detonations as traveling impulses with embedded reaction zones, and vortices as dynamically evolving structures with multiscale interactions. Using a modified version of OpenFOAM’s AMR capabilities, we replicate well-known test cases including the Sod shock tube, Mach 3 supersonic flow over a 30° compression ramp, and the forward-facing step. Additionally, we examine experimental shock–boundary layer interactions involving oblique-to-normal shock transitions over similar geometries. Both inviscid and RANS simulations using the Spalart–Allmaras model are present. Results are benchmarked against fixed-grid simulations to assess AMR’s ability to resolve key features with reduced computational cost. This study quantifies the strengths and limitations of AMR in capturing complex nonlinear dynamics in compressible reactive and non-reactive flows.