Study on the finite element scheme for fluid flows with free interface
Project/Area Number  10640111 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Toyama University 
Principal Investigator 
OHMORI Katsushi Toyama University, Faculty of Education, Professor, 教育学部, 教授 (20110231)

CoInvestigator(Kenkyūbuntansha) 
IKEDA Hideo Toyama University, Faculty of Science, Associated Professor, 理学部, 助教授 (60115128)

Project Period (FY) 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,300,000 (Direct Cost : ¥3,300,000)
Fiscal Year 1999 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1998 : ¥2,500,000 (Direct Cost : ¥2,500,000)

Keywords  Finite element method / Free interface / Incompressible fluid / Twofluid flows / Surface tension / Convergence of the interface 
Research Abstract 
This study has been carried out during 19981999 in order to develop and analyze the finite element scheme for fluid flows with free interface, which are often found in nature and manay industrial processes. In 1998, we have considered a finite element scheme for twofluid flows with low ratio of densities. We assume that two fluids are both viscous, incompressible and immiscible. As the mathematical model for this problem we use the onefluid model assuming thr Boussinesq approximation to the NavierStokes equations. The interface is considered as the 0level Set of the pseudodensity function which is the Solution of the transport equation. We have proposed a mixed finite element scheme with P1 iso P2/P1 element for these equations. Especially, we have also proposed the reinitialization technique in the finite element scheme for the transport equation by using a double well potential. In 1999 we have considered the finite element method for twofluid flows with free interface including surface tension effect. Here we use the true twofluid flow system in order to deal the problems with the high ratios of density and viscosity. In general, the surface tension effect is represented by the line integral on the interface. In our study the surface tension effect is interpreted as a body force spread across the interfacial region with a finite thickness. On the other hand, as the mathematical analysis of the finite element scheme for twofluid flows we have considered the convergence of the approximate interface. In fact, estimating the LィイD1pィエD1(Ω)norm of difference between the measure of positive value of the pseudodensity function and its approximation under the convergence of the finite element solution, we have prove it. Here we have used the Heaviside operator. The mathematical analysis of the total finite element scheme, however, is our theme in the near future.

Report
(3results)
Research Output
(18results)