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Arch Computat Methods Eng (2018) 25:691–706
DOI 10.1007/s11831-017-9213-8
ORIGINAL PAPER
A Higher‑Order Chimera Method for Finite Volume Schemes
Luis Ramírez
1
· Xesús Nogueira
1
· Pablo Ouro
2
· Fermín Navarrina
1
·
Sofiane Khelladi
3
· Ignasi Colominas
1
Received: 4 January 2017 / Accepted: 17 January 2017 / Published online: 14 February 2017
© CIMNE, Barcelona, Spain 2017
Moreover, the use of a single body-fitted mesh for the
simulation of flows with moving domains, requires the
deformation of the existing grid or the generation of a new
one at each time step. This procedure is highly demand-
ing in terms of computational cost for relatively large body
motions. For simple movement patterns, such as rotat-
ing domains or sliding planes, it is possible to use sliding
mesh techniques [1, 2]. In these cases, the computational
domain is divided into two subdomains, namely moving
and static subdomains. The information is transferred from
one domain to the other through their interface, by using
suitable interpolation techniques [1, 2].
A different approach in the simulation of moving bodies
is the Immersed Boundary (IB) method, first introduced by
Peskin [3] for the simulation of heart valves. Cartesian rec-
tangular meshes are commonly used in the IB approach and
they are decoupled from the immersed body mesh. Lately,
IB has also been adapted to unstructured meshes [4]. In
the classical IB approach, the boundary is introduced as
a forcing term in the governing equations. These methods
are attractive because of their simplicity. However, the
major drawbacks are the occurrence of non-divergence-free
velocities in incompressible flows [5], non-physical pres-
sure oscillations in compressible flows, and the difficulty to
get high-order accuracy near the walls [6]. A different class
of IB methods is the cut-cell method introduced by Clarke
[7], which does not exhibit of these problems. In the cut-
cell method the immersed boundaries cut the mesh, creat-
ing a set of irregularly shaped cells upon which the equa-
tions are discretized. A drawback of this approach is the
increased complexity, compared to the classical IB meth-
ods, since the original mesh needs to be cut by the moving
bodies every time step, which forces to recompute the geo-
metrical information and the integration points.
Abstract In this work a higher-order accurate finite vol-
ume method for the resolution of the Euler/Navier–Stokes
equations using Chimera grid techniques is presented. The
formulation is based on the use of Moving Least Squares
approximations in order to obtain higher-order accurate
reconstruction and connectivity between the overlapped
grids. The accuracy and performance of the proposed
methodology is demonstrated by solving different bench-
mark problems.
1 Introduction
The development of numerical methods for the simulation
of problems involving highly complex geometries, which
are frequent in many engineering problems, remains a
very active research field in computational fluid dynamics
(CFD). For these problems, the construction of multi-block
structured meshes, when possible, is highly time consum-
ing. In this context the use of unstructured grids becomes
competitive but, unfortunately, this kind of mesh typology
requires the use of more complex schemes when higher-
order approximations are desired.
* Luis Ramírez
luis.ramirez@udc.es
1
Group of Numerical Methods in Engineering, Universidade
da Coruña, Campus de Elviña, 15071 A Coruña, Spain
2
Hydro-Environmental Research Centre, School
of Engineering, Cardiff University, The Parade,
Cardiff CF24 3AA, UK
3
Laboratoire de Dynamique des Fluides, Arts et Métiers
ParisTech, 151 Boulevard de l’Hôpital, 75013 Paris, France
@Phil_Robichaud
@deepthiw
@JoseServera