A simple Eulerian finite-volume method for compressible fluids in domains with moving boundaries

Abstract

Abstract. We introduce a simple new Eulerian method for treatment of moving boundaries in compressible fluid computations. Our approach is based on the extension of the interface tracking method recently introduced in the context of multifluids. The fluid domain is placed in a rectangular computational domain of a fixed size, which is divided into Cartesian cells. At every discrete time level, there are three types of cells: internal, boundary, and external ones. The numerical solution is evolved in internal cells only. The numerical fluxes at the cells near the boundary are computed using the technique from [A. Chertock, S. Karni and A. Kurganov, M2AN Math. Model. Numer. Anal., to appear] combined with a solid wall ghost-cell extrapolation and an interpolation in the phase space. The proposed computational framework is general and may be used in conjunction with one's favorite finite-volume method. The robustness of the new approach is illustrated on a number of one-and two-dimensional numerical examples.

A Second-Order Finite-Difference Method for Compressible Fluids in Domains with Moving Boundaries

“…A simple FV method based on a Cartesian grid for the 1-D and 2-D compressible Euler equations in domains with solid moving boundaries was introduced in [8]. This FV method is an extension of the interface tracking method proposed in [7] for compressible multi-fluids.…”

A multiscale method for compressible liquid-vapor flow with surface tension

“…The surface tension coefficient γ is taken from the set { 0, 0.003, 0.006 }, d = 3, κ = 0.5, and the parameters for the van der Waals equation of state as in (4). Figure 7 shows the specific volumes and figure 8 velocity distributions.…”

“…Table 1 for a summary). In particular equation (7) is fulfilled for the van der Waals pressure (3) and constants in (4). A coarse grid of 30 × 30 × 30 cells is used, the polynomial order is N = 2 leading to a (formally) third-order scheme.…”

“…In our approach, this cell is filled with an extrapolation of the states in neighboring elements of the same phase. We employ a method similar to the one described by Chertock and Kurganov [4].…”

“…The setting is as in the previous example and the initial states are detailed in Table 2. The pressure function is described in (3), (4). The computational domain is discretized with a grid of 30 × 30 × 30 hexahedral elements.…”