TY - JOUR
T1 - Symbolic Computation as a Tool for High-Order Long-Wave Stability Analysis of Thin Film Flows with Coupled Transport Processes
AU - Lange, U.
AU - Nandakumar, K.
AU - Raszillier, H.
N1 - Funding Information:
We thank Professor F. Durst for his support of this work and his suggestions on the subject. U. Lange gratefully acknowledges the support of the Alexander von Humboldt Foundation by a Feodor Lynen Research Fellowship.
PY - 1999/3/20
Y1 - 1999/3/20
N2 - Many fundamental studies based on the evolution equations derived by long-wave approximation have contributed to the fact that the dynamics of a thin film flowing down an inclined plane is now one of the best-understood problems of hydrodynamic stability. In most engineering applications however, the stability behaviour of the film flow is modified by complex coupled transport processes, and because of the huge amount of algebra needed to derive the evolution equations in these cases, an investigation by numerical methods is often preferred by engineers. In this paper, we illustrate how computer algebra techniqes can be used to derive and analyse long-wave evolution equations even for very complex situations automatically, thus making the advantages of symbolic solutions available for such applications. Using these methods, higher-order approximations can also be obtained automatically. These are of interest since they can provide heuristic estimates for - and extensions of - the range of validity of the long-wave approximation.
AB - Many fundamental studies based on the evolution equations derived by long-wave approximation have contributed to the fact that the dynamics of a thin film flowing down an inclined plane is now one of the best-understood problems of hydrodynamic stability. In most engineering applications however, the stability behaviour of the film flow is modified by complex coupled transport processes, and because of the huge amount of algebra needed to derive the evolution equations in these cases, an investigation by numerical methods is often preferred by engineers. In this paper, we illustrate how computer algebra techniqes can be used to derive and analyse long-wave evolution equations even for very complex situations automatically, thus making the advantages of symbolic solutions available for such applications. Using these methods, higher-order approximations can also be obtained automatically. These are of interest since they can provide heuristic estimates for - and extensions of - the range of validity of the long-wave approximation.
KW - Automated algorithms
KW - Hydrodynamic stability
KW - Nonlinear effects
KW - Numerical analysis
UR - http://www.scopus.com/inward/record.url?scp=0345917604&partnerID=8YFLogxK
U2 - 10.1006/jcph.1998.6160
DO - 10.1006/jcph.1998.6160
M3 - 文章
AN - SCOPUS:0345917604
SN - 0021-9991
VL - 150
SP - 1
EP - 16
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 1
ER -