1D Unsteady Shock-Tube Simulation — Nitrogen

High-fidelity simulation of unsteady compressible flows requires numerical schemes that capture shock discontinuities without introducing spurious oscillations.

Develop a TVD numerical scheme in MATLAB to simulate 1D unsteady compressible flow in a shock tube, and validate against commercial CFD.

Implemented a Total Variation Diminishing scheme with minmod flux limiter in MATLAB. Captured density, velocity, pressure, and temperature distributions through the shock wave. Conducted grid refinement studies to document convergence behavior and numerical dissipation.

Achieved second-order spatial accuracy. Validated MATLAB results against ANSYS Fluent, confirming quantitative agreement across all four flow parameters. Produced a structured CFD validation report.