Figure 3

Illustration of two streaming scenarios when the current cell B at \(\vec{x}\) (dashed) and upwind cell A (dotted) at \(\vec{x}+{\vec{e}}_{i*}\delta t\) are both boundary cells. A parameter G is introduced to distinguish these two cases. (a) \({\mathcal{P}}_{B}>{\mathcal{P}}_{A}\), G = 1. The receiving particles are streamed from the upwind cell. Because the fluid fraction of B is smaller than that of cell A, only \(\frac{1-{\mathcal{P}}_{B}}{1-{\mathcal{P}}_{A}}{n{^{\prime}}}_{Ai}\) particles of cell A can stream into cell B and no bounced-back particles. (b) \({\mathcal{P}}_{B}<{\mathcal{P}}_{A}\), G=0. The receiving particles consists of two parts: streamed from the upwind cell A (n′_Ai) and the bounced-back particles from the current cell \(\frac{{\mathcal{P}}_{A}-{\mathcal{P}}_{B}}{1-{\mathcal{P}}_{B}}{n{^{\prime}}}_{Bi}\)∗ in the opposite direction.