Abstract—In this work, we developed a finite volume method code to handle the flow field problem of the one-dimensional unsteady Euler equations caused by the moving contact discontinuity interface between two different species on both sides of the shock tube. The derived additional energy conservation equation introduces a non-conservative term. It is crucial to reduce non-physical numerical oscillations and enhance shock-capturing capability and computational accuracy, especially for high-resolution problems. In this study, firstly, we extended the energy equation of the unsteady Euler equations to accommodate i species and considered different state equations. Based on the test results, it was found that the considered state equations did not improve the above issues. Furthermore, we attempted to extend the first-order flux limiter to second order and tested its effectiveness. The results showed that the quadratic term had minimal impact on the entire computation process in gradient calculations. Hence, attempting to improve the flux limiter through this approach was deemed inappropriate.

Keywords—Euler equations, numerical oscillation, contact discontinuity, shock capturing, Runge-Kutta method, gradient method, flux limiter

Cite: Yu-Tso Li, Tzong-Hann Shieh, "Study on New Methods for Accurate Modeling of Energy Equation with Multi Species," International Journal of Applied Physics and Mathematics, vol. 14, no. 3, pp. 99-105, 2024.

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