A Meshless Approach to Capturing Moving Interfaces in Passive Transport Problems
L. Mai-Cao; and T. Tran-Cong

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 31, No. 3, pp. 157-188, 2008
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Keywords Level set method, meshless method, radial basis functions, IRBFN, moving interfaces, passive transport, Taylor-IRBFN, Semi-Lagrangian approach.
Abstract This paper presents a new meshless numerical approach to solving a special class of moving interface problems known as the passive transport where an ambient flow characterized by its velocity field causes the interfaces to move and deform without any influences back on the flow. In the present approach, the moving interface is captured by the level set method at all time as the zero contour of a smooth function known as the level set function whereas one of the two new meshless schemes, namely the SL-IRBFN based on the semi-Lagrangian method and the Taylor-IRBFN scheme based on Taylor series expansion, is used to solve a convective transport equation for advancing the level set function in time. In addition, a mass correction is introduced after the reinitialization step to ensure mass conservation. Some basic tests are preformed to verify the accuracy and stability of the new numerical schemes which are then applied to simulate bubbles moving, stretching and merging in an ambient flow to demonstrate the performance of the new meshless approach.
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