TY - JOUR
T1 - A Second-Order Finite-Difference Method for Compressible Fluids in Domains with Moving Boundaries
AU - Alina Chertock, Armando Coco, Alexander Kurganov & Giovanni Russo
JO - Communications in Computational Physics
VL - 1
SP - 230
EP - 263
PY - 2018
DA - 2018/01
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2016-0133
UR - https://global-sci.org/intro/article_detail/cicp/10526.html
KW - Compressible fluids, Euler equations of gas dynamics, ghost-cell extrapolation, moving boundaries, finite-difference shock-capturing methods.
AB - <p style="text-align: justify;">In this paper, we describe how to construct a finite-difference shock-capturing
method for the numerical solution of the Euler equation of gas dynamics on
arbitrary two-dimensional domain Ω, possibly with moving boundary. The boundaries
of the domain are assumed to be changing due to the movement of solid objects/obstacles/walls.
Although the motion of the boundary could be coupled with
the fluid, all of the numerical tests are performed assuming that such a motion is prescribed
and independent of the fluid flow. The method is based on discretizing the
equation on a regular Cartesian grid in a rectangular domain Ω<sub>R</sub> ⊃ Ω. We identify
inner and ghost points. The inner points are the grid points located inside Ω, while
the ghost points are the grid points that are outside Ω but have at least one neighbor
inside Ω. The evolution equations for inner points data are obtained from the discretization
of the governing equation, while the data at the ghost points are obtained
by a suitable extrapolation of the primitive variables (density, velocities and pressure).
Particular care is devoted to a proper description of the boundary conditions for both
fixed and time dependent domains. Several numerical experiments are conducted to
illustrate the validity of the method. We demonstrate that the second order of accuracy
is numerically assessed on genuinely two-dimensional problems.</p>