A SEMI-LAGRANGIAN PARTICLE LEVEL SET FINITE ELEMENT METHOD FOR INTERFACE PROBLEMS

作者：Bermejo Rodolfo^*; Luis Prieto Juan

来源：SIAM Journal on Scientific Computing, 2013, 35(4): A1815-A1846.

DOI：10.1137/110830587

• level set
• semi-Lagrangian
• reinitialization
• finite elements
• incompressible flows
• interfaces

We present a quasi-monotone semi-Lagrangian particle level set (QMSL-PLS) method for moving interfaces. The QMSL method is a blend of first order monotone and second order semi-Lagrangian methods. The QMSL-PLS method is easy to implement, efficient, and well adapted for unstructured, either simplicial or hexahedral, meshes. We prove that it is unconditionally stable in the maximum discrete norm, parallel to . parallel to(h,infinity) and the error analysis shows that when the level set solution u(t) is in the Sobolev space W-r+1,W-infinity(D), r %26gt;= 0, the convergence in the maximum norm is of the form (KT/Delta t) min(1, Delta t parallel to v parallel to(h,infinity) /h)((1-alpha)h(p) + h(q)), p = min(2, r + 1), and q = min(3, r + 1), where v is a velocity. This means that at high CFL numbers, that is, when Delta t %26gt; h, the error is O((1-alpha)h(p)+h(q))Delta t), whereas at CFL numbers less than 1, the error is O((1-alpha)h(p-1) + h(q-1))). We have tested our method with satisfactory results in benchmark problems such as the Zalesak%26apos;s slotted disk, the single vortex flow, and the rising bubble.

• 出版日期2013