Sod Shock tube solver - HHLC Based

D compressible Euler solver — MUSCL-HLLC with TVD limiters and optional H₂/O₂ Arrhenius chemistry. Validated on Sod Shock Tube.

This MATLAB solver simulates 1D compressible inviscid flow using the Euler equations. It is built around an HLLC approximate Riemann solver (Toro, 2009) combined with a MUSCL reconstruction scheme and TVD slope limiters (Van Leer, Van Albada, Minbee) to achieve second-order spatial accuracy while avoiding spurious oscillations near discontinuities.

The solver supports two operating modes: without chemical reactions, for classical benchmark validation, and with chemical reactions, where a reactive scalar λ evolves according to single-step Arrhenius kinetics and feeds back into the total energy of each cell through a variable ratio of specific heats γ.

Key features:

• HLLC flux (Variant 1 and 2) with pressure-based or enthalpy-based wave speed estimation
• MUSCL reconstruction with selectable slope limiter (Van Leer, Van Albada, Minbee)
• Adaptive time-stepping via CFL condition
• Boundary conditions: reflective and transmissive
• Validated against all four Sod Shock Tube test cases from Toro (2009), including the most demanding high-pressure ratio case
• Interactive GUI (.mlapp) for parameter control and real-time visualization

This solver was developed as the 1D foundation of a larger project aimed at simulating a Rotating Detonation Engine (RDE) combustor. The 2D extension is available separately on MATLAB File Exchange.

Requirements: MATLAB R2020b or later. No additional toolboxes required.