A thermally robust gradient-based finite-difference scheme for multicomponent compressible reacting flows

College of Computing, Mohammed VI Polytechnic University (UM6P), Benguerir, Morocco

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Published online: 22 May 2026

Abstract

We develop a high-order gradient-based reconstruction method for multispecies, chemically reacting compressible flows with temperaturedependent thermodynamics. The approach extends Chamarthi’s gradientbased reconstruction strategy to thermally perfect mixtures, where all thermochemical and transport properties are evaluated through Cantera. Highorder gradients are computed once per time step and reused for inviscid, viscous, and limiting operations, reducing the cost of multicomponent diffusion and heat-transfer evaluations while preserving accuracy. Shock robustness is ensured through a monotonicity-preserving limiter formulated in characteristic space. The resulting scheme delivers high-order accuracy in smooth regions and sharp, stable resolution of shocks and material interfaces. Benchmark tests—including viscous shock tubes, double Mach reflection, and shock–bubble interaction—demonstrate reduced dissipation and lower computational cost compared with WENO-type schemes.