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ABSTRACT
In most applications of computational fluid dynamics (CFD), it is very important to correctly project the interaction phenomena when we compute the typical discontinuous structure. Numerical methods for the conservation law are usually divided into two kinds: One is the “single stepping method”; another is the “semidiscrete scheme”. When the semidiscrete scheme handles the issues of high accuracy and operational process without oscillations, it is a very successful method. In this article, we consider the one-dimensional Euler equations for the Riemann problem of a typical shock tube without external active force to improve the nonphysical numerical oscillation problem near the contact discontinuity interface and shock wave. We try to improve the computational accuracy of numerical resolution of the Riemann problem and reduce nonphysical numerical oscillations through the AUSMDV numerical flux scheme with implementing distinct flux limiters and time-stepping methods. Using the conditions of single gas/dual gases, we carry out a series of comparisons for the accuracy of shock capturing as well as the capability of improving numerical oscillations.
Nomenclature
| CCFL | = | CFL number, Δt = (Δx/vmax)CCFL |
| e | = | specific internal energy, J/kg |
| E | = | specific energy, J/kg |
| F | = | frictionless flux vector, N/m2 |
| h | = | entropy, kJ/kg |
| i, j | = | step number of individual displacement |
| K | = | individual control volume, m3 |
| max | = | maximum |
| min | = | minimum |
| P | = | pressure, psi |
| Q | = | source term, N/m2 |
| r | = | specific local flux |
| R | = | gas constant, J/kg·K |
| s | = | average |
| s | = | switching function |
| t | = | time, s |
| T | = | temperature, K |
| u | = | velocity on x axis, m/s |
| U | = | vector of conservation variables, N/m2 |
| = | mean value of conserved variable vector | |
| vmax | = | maximum propagation velocity, m/s |
| V | = | volume, m3 |
| ∂V | = | unit surface, m2 |
| Wi | = | molar mass, kg/kmol |
| Yi | = | mass fraction (=ρi/ρ) |
| γ | = | ratio of specific heats |
| Δ | = | difference |
| ς | = | specific volume (=1/ρ), m3/kg |
| ν | = | courant number (=vmax Δt/Δx) |
| ρ | = | density, kg/m3 |
| ϕ | = | conservation variables |
| ϕ | = | limit function |
| Φ | = | flux function, N/m2 |
Nomenclature
| CCFL | = | CFL number, Δt = (Δx/vmax)CCFL |
| e | = | specific internal energy, J/kg |
| E | = | specific energy, J/kg |
| F | = | frictionless flux vector, N/m2 |
| h | = | entropy, kJ/kg |
| i, j | = | step number of individual displacement |
| K | = | individual control volume, m3 |
| max | = | maximum |
| min | = | minimum |
| P | = | pressure, psi |
| Q | = | source term, N/m2 |
| r | = | specific local flux |
| R | = | gas constant, J/kg·K |
| s | = | average |
| s | = | switching function |
| t | = | time, s |
| T | = | temperature, K |
| u | = | velocity on x axis, m/s |
| U | = | vector of conservation variables, N/m2 |
| = | mean value of conserved variable vector | |
| vmax | = | maximum propagation velocity, m/s |
| V | = | volume, m3 |
| ∂V | = | unit surface, m2 |
| Wi | = | molar mass, kg/kmol |
| Yi | = | mass fraction (=ρi/ρ) |
| γ | = | ratio of specific heats |
| Δ | = | difference |
| ς | = | specific volume (=1/ρ), m3/kg |
| ν | = | courant number (=vmax Δt/Δx) |
| ρ | = | density, kg/m3 |
| ϕ | = | conservation variables |
| ϕ | = | limit function |
| Φ | = | flux function, N/m2 |
Acknowledgments
We are grateful to Prof. Meng-Rong Li and Ms. Yu-Tso Li for their assistance in this study.