One-dimensional compressible gas dynamics calculations using the Boltzmann equation
One-dimensional compressible gas dynamics calculations using the Boltzmann equation
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DOI：
10.1016/0021-9991(81)90235-7
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发表时间：
1981-07
影响因子：
4.1
通讯作者：
R. Reitz
中科院分区：
文献类型：
--
作者：
R. Reitz
用一种新的方法求解玻尔兹曼方程，进行了一维无粘气体动力学计算。数值方法是明确的，是基于气体动力学理论的概念。通过对分子速度分布函数进行数值积分，计算出气体密度、速度和温度。反过来，这是由玻尔兹曼方程计算使用算子分裂的方法。结果表明，该基本算法是有效且无条件稳定的。对单组分双原子理想气体的初边值问题进行了验证。这些问题包括黎曼激波管问题和固定壁面在入射马赫数toM= 10以上范围内的激波反射。结果表明，对于某些问题，该方法比标准有限差分方法具有明显的优势。在溶液中振荡最小的情况下，能很好地分解激波，得到比通常稳定性极限大一个数量级的准确结果。该方法在接近热力学平衡的流动区域表现最好，而在远离平衡的区域则是一阶精确的，这可以从动力学理论的论点中预测出来。
One-dimensional inviscid gas dynamics computations are made using a new method to solve the Boltzmann equation. The numerical method is explicit and is based on concepts from the kinetic theory of gases. The gas density, velocity and temperature are computed by integrating numerically the molecular velocity distribution function. This in turn is computed from the Boltzmann equation using an operator splitting approach. The basic algorithm is shown to be efficient and unconditionally stable. The method is tested for a single component diatomic ideal gas on initial-boundary value problems. These include the Riemann shock-tube problem and shock wave reflection from a stationary wall for a range of incident Mach numbers up toM= 10. The results show that the method can offer significant advantages over standard finite difference methods for certain problems. Shock waves are resolved well with minimal oscillations in the solution, and accurate results are obtained with Courant numbers an order of magnitude larger than the usual stability limit. The method performs best in regions of the flow which are close to thermodynamic equilibrium and is first order accurate in regions which are far from equilibrium, as would be predicted from kinetic theory arguments.