In this paper, general motion of a two-dimensional body is modeled using a new moving mesh concept. Solution domain is divided into the three zones. The first zone, with a circular boundary, includes the moving body and facilitates the rotational motion of it. The second zone, with a square boundary, includes the first zone and facilitates the translational motion of the body. The third zone is a background grid in which the second zone moves. With this configuration of grids any two-dimensional motion of a body can be modeled with almost no grid insertion or deletion. However, in some stages of motion we merge or split a few number of elements. The discretization method is control-volume based finite-element, and the unsteady form of the Euler equations are solved using AUSM algorithm. To demonstrate the excellent performance of the present method two moving cases including rotational and translational motions are solved. The results show excellent agreement with experimental data or other numerical results.

1.
Goswami
,
A.
, and
Parpia
,
I. H.
, 1991, “
Grid Restructuring for Moving Boundaries
,” AIAA Paper No. 91-1589-CP.
2.
Trepanier
,
J. Y.
,
Reggio
,
M.
,
Paraschiviou
,
M.
, and
Camarero
,
R.
, 1992, “
Unsteady Euler Solution for Arbitrary Moving Bodies and Boundaries
,” AIAA Paper No. 92-0051-1992.
3.
Batina
,
J. T.
, 1990, “
Unsteady Euler Airfoil Solutions Using Unstructured Dynamic Meshes
,”
AIAA J.
0001-1452,
28
(
8
), pp.
1381
1388
.
4.
Pirzadeh
,
S. Z.
, 1999, “
An Adaptive Unstructured Grid Method by Grid Subdivision, Local Remeshing and Grid Movement
,” 14th AIAA, AIAA Paper No. 99-3255.
5.
Batina
,
J. T.
, 1991, “
Unsteady Euler Algorithm with Unstructured Dynamic Mesh for Complex Airfoil Aerodynamic Analysis
,”
AIAA J.
0001-1452,
29
(
3
), pp.
327
333
.
6.
Tsai
,
H. M.
,
Wong
,
A. S. F.
,
Cai
,
J.
,
Zhu
,
Y.
, and
Liu
,
F.
, 2001, “
Unsteady Flow Calculations with a Parallel Multi-block Moving Mesh Algorithm
,”
AIAA J.
0001-1452,
39
(
6
), pp.
1021
1029
.
7.
Jahangirian
,
A.
, and
Hadidoolabi
,
M.
, 2004, “
An Implicit Solution of the Unsteady Navier-Stokes Equations on Unstructured Moving Grids
,” 24th International Congress of the Aeronautical Science, ICAS, Yokohama, Japan.
8.
Hase
,
J. E.
,
Anderson
,
D. A.
, and
Parpia
,
I. H.
, 1991, “
A Delaunay Triangulation Method and Euler Solver for Bodies in Relative Motion
,” AIAA Paper No. 91-1590-CP.
9.
Zheng
,
Y.
,
Lewis
,
R. W.
, and
Gethin
,
D. T.
, 1996, “
Three-Dimensional Unstructured Mesh Generation Part 1-3
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
134
, pp.
249
310
.
10.
Formaggia
,
L.
,
Peraire
,
J.
, and
Morgan
,
K.
, 1988, “
Simulation of a Store Separation Using the Finite Element Method
,”
J. Turbomach.
0889-504X,
12
, pp.
175
181
.
11.
Steger
,
J. L.
,
Dougherty
,
F. C.
, and
Benek
,
J. A.
, 1983, A Chimera Grid Scheme, in Advances in Grid Generation, American Society of Mechanical Engineers, FED, New York, Vol.
5
, pp.
59
69
.
12.
Benek
,
J. A.
,
Buning
,
P. G.
, and
Steger
,
J. L.
, 1985, “
A 3-D Chimera Grid Embedding Technique
,” AIAA Paper No. 85-1523.
13.
Nakahashi
,
K.
,
Togashi
,
F.
, and
Sharov
,
D.
, 2000, “
Intergrid-Boundary Definition Method for Overset Unstructured Grid Approach
,”
AIAA J.
0001-1452,
38
(
11
), pp.
2077
2084
.
14.
Kallinderis
,
Y.
,
Khawaja
,
A.
, and
Mc-Morris
,
H.
, 1996, “
Hybrid Prismatic/Tetrahedral Grid Generation for Complex Geometries
,”
AIAA J.
0001-1452,
34
, pp.
291
298
.
15.
Coirier
,
W. J.
, and
Jorgenson
,
P. C. E.
, 1996, “
A Mixed Volume Grid Approach for the Euler and Navier-Stokes Equations
,” AIAA Paper No. 96-0762.
16.
Karman
,
S. L.
, 1995, “
SPLITFLOW: A 3D Unstructured Cartesian/Prismatic Grid CFD Code for Complete Geometries
,” AIAA Paper No. 95-0343.
17.
Zhang
,
L. P.
,
Zhang
,
H. X.
, and
Gao
,
S. C.
, 1997, “
A Cartesian/Unstructured Hybrid Grid Solver and its Applications to 2D/3D Complex Inviscid Flow Fields
,”
Proceedings of the 7th International Symposium on CFD
, Beijing, China, pp.
347
352
.
18.
Zhang
,
L. P.
,
Yang
,
Y. J.
, and
Zhang
,
H. X.
, 2000, “
Numerical Simulations of 3D Inviscid/Viscous Flow Fields on Cartesian/Unstructured/Prismatic Hybrid Grids
,”
Proceedings of the 4th Asian CFD Conference
, Mianyang, Sichuan, China.
19.
Murman
,
S.
,
Aftosmis
,
M.
, and
Berger
,
M.
, 2003, “
Implicit Approaches for Moving Boundaries in a 3D Cartesian Method
,” AIAA Paper No. 2003-1119.
20.
Zhang
,
L. P.
, and
Wang
,
Z. J.
, 2004, “
A Block LU-SGS Implicit Dual Time-stepping Algorithm for Hybrid Dynamic Meshes
,”
Comput. Fluids
0045-7930,
33
, pp.
891
916
.
21.
Tezduyar
,
T. E.
,
Behr
,
M.
,
Mittal
,
S.
, and
Liou
,
J.
, 1992, “
A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces—The Deforming-Spatial-Domain/Space-Time Procedure Part II: Computation of Free-Surface Flows, Two-Liquid Flows, and Flows with Drifting Cylinders
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
94
, pp.
353
371
.
22.
Mittal
,
S.
, and
Tezduyar
,
T. E.
, 1992, “
A Finite Element Study of Incompressible Flows Past Oscillating Cylinders and Airfoils
,”
Int. J. Numer. Methods Fluids
0271-2091,
15
, pp.
1073
1118
.
23.
Behr
,
M.
, and
Tezduyar
,
T.
, 1999, “
The Shear-Slip Mesh Update Method
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
174
, pp.
261
274
.
24.
Behr
,
M.
, and
Tezduyar
,
T.
, 2001, “
Shear-Slip Mesh Update in 3D Computation of Complex Flow Problems with Rotating Mechanical Components
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
, pp.
3189
3200
.
25.
Lin
,
C. Q.
, and
Pahlke
,
K.
, 1994, “
Numerical Solution of Euler Equations for Aerofoils in Arbitrary Unsteady Motion
,”
Aeronaut. J.
0001-9240, June/July, pp.
207
214
.
26.
Truilo
,
J. G.
, and
Trigger
,
K. R.
, 1961, “
Numerical Solution of the One-Dimensional Hydrodynamic Equations in an Arbitrary Time-Dependent Coordinate System
,” Univ. of California, Lawrence Radiation Lab. Report UCLR-6522.
27.
Thomas
,
P. D.
, and
Lombard
,
C. K.
, 1978, “
The Geometric Conservation Law—A Link Between Finite-Difference and Finite-Volume Methods of Flow Computation on Moving Grids
,” AIAA Paper No. 78-1208.
28.
Thomas
,
P. D.
, and
Lombard
,
C. K.
, 1979, “
Geometric Conservation Laws and its Application to Flow Computation on Moving Grids
,”
AIAA J.
0001-1452,
17
, pp.
1030
1037
.
29.
Zhang
,
H.
,
Reggio
,
M.
,
Trepanier
,
J. Y.
, and
Camarero
,
R.
, 1993, “
Descrete Form of the GCL for moving Meshes and its Implementation in CFD Schemes
,”
Comput. Fluids
0045-7930,
22
(
1
), pp.
9
23
.
30.
Karimian
,
S. M. H.
,
Amoli
,
A.
, and
Mazaheri
,
K.
, 2002, “
Control-Volume Finite-Element Method for the Solution of 2D Euler Equations on Unstructured Moving Grids
,”
Iranian J. Sci. Technol., Trans. B
,
26
(
B3
), pp.
465
476
.
31.
Roe
,
P. L.
, 1981, “
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
,”
J. Comput. Phys.
0021-9991,
43
, pp.
357
372
.
32.
Liou
,
M.
, and
Steffen
,
C. J.
, 1993, “
A New Flux Splitting Scheme
,”
J. Comput. Phys.
0021-9991,
107
, pp.
23
39
.
33.
Karimian
,
S. M. H.
, and
Schneider
,
G. E.
, 1995, “
Pressure-Based Control-Volume Finite-Element Method for Flow at All Speeds
,”
AIAA J.
0001-1452,
33
(
11
), pp.
1611
1618
.
34.
Compendium of Unsteady Aerodynamic Measurements
, Report No. AGARD-R-702, 1982.
35.
Gaitonde
,
A. L.
, and
Fiddes
,
S. P.
, 1995, “
A Comparison of a Cell-Centre Method and a Cell-Vertex Method for the Solution of Two-dimensional Unsteady Euler Equations on a Moving Grid
,”
Am. Antiq.
0002-7316,
209
, pp.
203
213
.
You do not currently have access to this content.