A fractional step method to compute a class of compressible gas–liquid flows

TLDR: In this article, the authors present some algorithms dedicated to the computation of numerical approximations of a class of two-fluid two-phase flow models and give the main properties of these models.

About: This article is published in Computers & Fluids.The article was published on 2012-02-15 and is currently open access. It has received 48 citations till now. The article focuses on the topics: Relaxation (approximation) & Uniqueness.

Figures

Figure 11: Heated wall: y-profile of the gas density ρg at three distinct times T = T1 (dotted line), T2 (dashed line), T5 (plain line), at: x = 2. The small cavity in the wall boundary corresponds to −0.25 < y < 0.

Table 1: : Initial condition for the first Riemann problem and intermediate states.

Figure 3: Approximate solution of the second Riemann problem obtained with 100000 cells and the exact solution (ex.) at time t = 1.4 10−4. Top left: liquid fraction, top right: pressures, bottom left: densities, bottom right: velocities.

Figure 2: L1 norm of the error for the first Riemann problem. Plain lines: gas, dotted lines: liquid. Liquid mass fraction (crosses), velocities (squares), pressures (triangles), densities (circles). Meshes contain 500000, 250000, 50000, 5000, 500 and 50 regular cells.

Figure 12: Heated wall: y-profiles of gas and liquid pressures Pg, Pl at three distinct times T = T1 (dotted line), T2 (dashed line), T5 (plain line), at: x = 2. The small cavity in the wall boundary corresponds to −0.25 < y < 0.

Figure 7: Pressure relaxation substep: measured L1 norm of the error for the liquid pressure (straight line) and the gas pressure (dotted line) at time T = 10−5 as a function of ∆t/τ2 = {10, 1, 10−1, 10−2, 10−3}. Implicit scheme (20) (circles) versus half-implicit scheme (squares).