Browsing by Author "Ito, Kazufumi"

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A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains
(2009-04-20)
Ito, Kazufumi
;
Lai, Ming-Chih
;
Li, Zhilin
;
應用數學系
;
Department of Applied Mathematics
An augmented method based on a Cartesian grid is proposed for the incompressible Navier-Stokes equations in irregular domains. The irregular domain is embedded into a rectangular one so that a fast Poisson solver can be utilized in the projection method. Unlike several methods suggested in the literature that set the force strengths as unknowns, which often results in an ill-conditioned linear system, we set the jump in the normal derivative of the velocity as the augmented variable. The new approach improves the condition number of the system for the augmented variable significantly. Using the immersed interface method, we are able to achieve second order accuracy for the velocity. Numerical results and comparisons to benchmark tests are given to validate the new method. A lid-driven cavity flow with multiple obstacles and different geometries are also presented. (C) 2008 Elsevier Inc. All rights reserved.
An augmented approach for Stokes equations with a discontinuous viscosity and singular forces
(2007-03-01)
Li, Zhilin
;
Ito, Kazufumi
;
Lai, Ming-Chih
;
應用數學系
;
Department of Applied Mathematics
For Stokes equations with a discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, it is known that the pressure is discontinuous and the velocity is non-smooth. It has been shown that these discontinuities are coupled together, which makes it difficult to obtain accurate numerical solutions. In this paper, a new numerical method that decouples the jump conditions of the fluid variables through two augmented variables has been developed. The GMRES iterative method is used to solve the Schur complement system for the augmented variables that are only defined on the interface. The augmented approach also rescales the Stokes equations in such a way that a fast Poisson solver can be used in each iteration. Numerical tests using examples that have analytic solutions show that the new method has average second order accuracy for the velocity in the infinity norm. An example of a moving interface problem is also presented. (c) 2006 Elsevier Ltd. All rights reserved.