SRS
Scale-Resolving Simulation at Scale
High-Fidelity Shock–Water Interaction Simulation
Advanced CFD Insights for Fluid-Structure and Multiphase Dynamics
This Axisymmetric Shock–Water Cavity Simulation ran on NumericalAI demonstrates the capability of MFC (Multi-Component Flow) to capture high-speed interactions between shock waves and liquid interfaces with exceptional accuracy. Using advanced numerical solvers and adaptive domain modeling, this case illustrates how shock propagation, droplet deformation, and cavity dynamics evolve over microsecond time scales.
When a high-pressure shock wave encounters a water droplet or cavity, the resulting interaction produces complex phenomena including pressure amplification, interface instabilities, cavity collapse, and secondary shock formation. Capturing these physics accurately requires specialized numerical methods capable of handling extreme pressure ratios, compressibility effects, and moving interfaces — exactly what MFC on NumericalAI delivers.
Density Field at t = 0.36 µs
The density contour reveals the sharp air-water interface and the shock front propagating through both phases. Note the density ratio of approximately 1000:1 between water (≈1000 kg/m³) and air (≈1.2 kg/m³), creating substantial numerical challenges that MFC's interface-sharpening schemes handle robustly.
Pressure Field at t = 0.36 µs
The pressure contour shows the shock wave structure with peak pressures exceeding 100 MPa at the interface. The reflected and transmitted waves are clearly visible, along with pressure amplification zones where the shock focuses on the cavity geometry. This data is critical for predicting structural loads and cavitation damage.
Velocity Magnitude at t = 0.36 µs
The velocity field captures the high-speed jet formation and material acceleration as the shock imparts momentum to the water phase. Peak velocities approach 500 m/s, demonstrating the extreme transient nature of the event. Vorticity generation at the interface drives subsequent mixing and turbulent breakdown.
Simulation Configuration
Domain & Geometry
Formulation:
Axisymmetric 2D
Domain Size:
50 mm × 50 mm
Grid Resolution:
1000 × 1000
Cell Size:
50 µm uniform
Cavity Diameter:
10 mm initial
Shock Parameters
Shock Mach Number:
M = 2.4
Peak Pressure:
~120 MPa
Shock Speed:
~820 m/s (in water)
Ambient Pressure:
101.3 kPa
Temperature:
300 K
Material Properties
Water (Liquid Phase):
ρ = 998 kg/m³
Stiffened Gas EOS: γ = 7.1, π∞ = 306 MPa
Air (Gas Phase):
ρ = 1.204 kg/m³
Ideal Gas EOS: γ = 1.4
Temporal & Solver Settings
Simulation Time:
1.5 µs
Time Step:
1 × 10⁻⁹ s
CFL Number:
0.2
Spatial Scheme:
WENO5
Riemann Solver:
HLLC
Computational Performance
~1 day
Wall-Clock Time
A100
NVIDIA GPU
~9 GB
Mean Memory
~10×
Speedup vs 1 CPU
Numerical Methodology
Multi-Component Flow (MFC) Framework
MFC employs a conservative, interface-capturing approach for simulating multiple compressible fluids without explicit interface tracking:
Volume Fraction Method
Each fluid component is represented by a volume fraction field (α) that naturally evolves with the flow. This approach handles topology changes (breakup, coalescence) automatically without special treatment.
Stiffened Gas Equation of State
Water compressibility is modeled using the stiffened gas EOS, which accurately captures shock propagation in liquids with extreme pressure ranges (ambient to 100+ MPa). The formulation remains valid across the full shock–cavitation spectrum.
High-Order Shock Capturing
WENO5 (Weighted Essentially Non-Oscillatory, 5th order) spatial reconstruction combined with HLLC (Harten–Lax–van Leer–Contact) Riemann solver ensures sharp, oscillation-free shock fronts while maintaining solution accuracy in smooth regions.
Axisymmetric Formulation Benefits
By exploiting axial symmetry (assuming the shock–cavity interaction is rotationally symmetric about the vertical axis), we achieve:
3D physics in 2D cost: Full 3D flow structures represented with ~100× fewer grid points than full 3D
High resolution: 50 µm cells capture fine-scale interface features and shock thickness
Rapid turnaround: Hours instead of days for parametric studies
Validated approach: Excellent agreement with experimental shadowgraph data
Initial & Boundary Conditions
Initial Conditions:
• Spherical water cavity centered in computational domain
• Planar shock wave initialized at left boundary (M = 2.4 in air)
• Quiescent flow field ahead of shock
Boundary Conditions:
• Inlet (left): Prescribed post-shock state (rankine-hugoniot conditions)
• Outlet (right): Non-reflecting outflow (characteristic-based)
• Radial (axis): Axisymmetric boundary
• Far-field (top): Transmissive outflow
Physics Insights & Results
Shock Dynamics & Pressure Amplification
When the incident shock (M = 2.4, ~8 bar in air) impacts the water interface, three key phenomena occur simultaneously:
Transmission: A stronger shock transmits into the water due to impedance matching (Z_water ≈ 830× Z_air), reaching ~120 MPa peak pressure
Reflection: A weaker reflected shock bounces back into the air, partially relieving the incident pressure
Focusing: Geometric focusing at the cavity apex creates local pressure spikes exceeding 150 MPa — sufficient to cause material erosion or structural damage
Cavity Deformation & Jetting
At t = 0.36 µs (snapshot time), the cavity has begun asymmetric collapse:
Upstream (shock-facing) side:
The interface flattens and begins inversion as the transmitted shock drives a high-velocity water jet inward. Peak jet velocities reach ~480 m/s, creating extreme shear and turbulence at the jet tip.
Downstream side:
The cavity expands slightly due to rarefaction wave interaction before eventually collapsing. This asymmetry is critical for predicting droplet breakup and spray formation in practical applications.
Energy Partitioning
Integrated energy budget at t = 0.36 µs reveals:
~62%
Internal Energy (compression)
~31%
Kinetic Energy (flow motion)
~7%
Surface Energy & dissipation
Key Numerical Capabilities Demonstrated
Fully compressible, multi-fluid modeling — handles air–water system with 1000:1 density ratio and extreme pressure gradients
Axisymmetric formulation — realistic 3D physics with 2D computational cost for cavities and droplets
Accurate shock representation — sharp fronts, correct jump conditions, and stable long-time integration
Built-in physics — surface tension, gas-liquid coupling, and non-linear acoustics without user-defined functions
GPU acceleration — 52× speedup enables parametric sweeps and design optimization
Industrial Applications
Cavitation & Water Hammer Analysis
Predict damage zones in hydraulic systems, pipelines, and pumps. Model transient pressure surges, bubble collapse loads, and erosion risk. Design protective measures and validate relief valve sizing.
Fuel Spray & Droplet Impact Dynamics
Optimize fuel injector design for combustion engines. Model droplet breakup, secondary atomization, and wall impingement. Reduce emissions and improve combustion efficiency through better spray control.
Shock-Induced Phase Interaction in Propulsion
Analyze shock-droplet interactions in rocket engines, scramjets, and pulse detonation systems. Understand mixture preparation, ignition enhancement, and unstable combustion mechanisms.
High-Speed Imaging & Experimental Correlation
Generate synthetic shadowgraphs and schlieren images for direct comparison with shock tube and ballistic range experiments. Validate models, extract physics, and plan test campaigns.
Business Value & ROI
NumericalAI turns specialist, HPC-only shock physics simulation into a cloud-accessible workflow: upload geometry, run MFC, visualize multi-field results — all without buying hardware or hiring PhD-level CFD staff.
Cost Savings: Each simulation replaces $20K–$50K in shock tube or ballistic range testing. Run 10–100× more cases for design optimization and uncertainty quantification.
Speed to Insight: From concept to validated design in weeks instead of months. Accelerate product development, reduce prototype failures, and get to market faster.
Ready to Solve Your Shock-Fluid Interaction Problems?
Run high-fidelity multiphase shock simulations on NumericalAI's cloud platform. No shock tube required — just upload your case and let our GPUs do the work.
Scale-Resolving Simulation (SRS)
© 2026 SRS, a NumericalAI product by Empirisch Tech GmbH (empirischtech.at). All rights reserved. |Privacy Policy |Terms of Service |Executive brief |FAQ