Fluorem/PR02R
PR02R: 2D turbulent case. F. Pacull, Lyon, France
Name 
PR02R 
Group 
Fluorem 
Matrix ID 
2336 
Num Rows

161,070 
Num Cols

161,070 
Nonzeros

8,185,136 
Pattern Entries

8,185,136 
Kind

Computational Fluid Dynamics Problem 
Symmetric

No 
Date

2010 
Author

F. Pacull 
Editor

T. Davis 
Structural Rank 
161,070 
Structural Rank Full 
true 
Num Dmperm Blocks

457 
Strongly Connect Components

457 
Num Explicit Zeros

0 
Pattern Symmetry

94.8% 
Numeric Symmetry

0% 
Cholesky Candidate

no 
Positive Definite

no 
Type

real 
Download 
MATLAB
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Notes 
CFD matrices from Francois Pacull, FLUOREM, in Lyon, France
We are dealing with CFD and more precisely steady flow
parametrization. The equations involved are the compressible
NavierStokes ones (RANS). These matrices are real, square and
indefinite, they correspond to the Jacobian with respect the
conservative fluid variables of the discretized governing
equations (finitevolume discretization). Thus they have a
block structure (corresponding to the mesh nodes: the block
size is the number of variables per mesh node), they are not
symmetric (however, their blockwise structure has a high level
of symmetry) and they often show some kind of hyperbolic
behavior. They have not been scaled or reordered.
They are generated through automatic differentiation of the
flow solver around a steady state. A right handside is also
given for each matrix: this represents the derivative of the
equations with respect to a parameter (of operation or shape).
Since they are generated automatically, they may have "silent"
variables: these are variables corresponding to an identity
submatrix associated with a null right handside, for example
one of the three velocity components in a 2D case, or the
turbulent variables in a "frozen" turbulence case.
We believe that these matrices are good test cases when
studying preconditioning methods for iterative methods, such as
block incomplete factorization, or when studying domain
decomposition methods or deflation. They are actually being
studied by a few researchers in France regarding numerical
methods, through the LIBRAERO research project of the ANR (national
research agency): ANR07TLOG011.
Francois Pacull, Lyon, France. fpacull at fluorem.com
Specific problem descriptions:
PR02R: 2D turbulent case
number of mesh nodes: 23010
block size: 7
variables: [rho,rho*u,rho*v,rho*w,rho*E,rho*k,rho*omega]
(rho v is "silent", the third row and column in each block
can be removed)
matrix order: 161070
nnz: 8185136
comments: This is a 2D turbulent case, dominated by
convection. The geometry is a RAE wing profile and the mesh
is Cshaped.
