TY - JOUR

T1 - A non-stiff boundary integral method for 3D porous media flow with surface tension

AU - Ambrose, David M.

AU - Siegel, Michael

N1 - Funding Information:
This work was supported by the NSF under Grant Nos. DMS-0708977 and DMS-0354560 (MS) and DMS-0926378 (DMA). Simulations were conducted on the NJIT computing cluster, supported by the NSF/MRI under Grant No. DMS-0420590.

PY - 2012/2

Y1 - 2012/2

N2 - We present an efficient, non-stiff boundary integral method for 3D porous media flow with surface tension. Surface tension introduces high order (i.e., high derivative) terms into the evolution equations, and this leads to severe stability constraints for explicit time-integration methods. Furthermore, the high order terms appear in non-local operators, making the application of implicit methods difficult. Our method uses the fundamental coefficients of the surface as dynamical variables, and employs a special isothermal parameterization of the interface which enables efficient application of implicit or linear propagator time-integration methods via a small-scale decomposition. The method is tested by computing the relaxation of an interface to a flat surface under the action of surface tension. These calculations employ an approximate interface velocity to test the stiffness reduction of the method. The approximate velocity has the same mathematical form as the exact velocity, but avoids the numerically intensive computation of the full Birkhoff-Rott integral. The algorithm is found to be effective at eliminating the severe time-step constraint that plagues explicit time-integration methods.

AB - We present an efficient, non-stiff boundary integral method for 3D porous media flow with surface tension. Surface tension introduces high order (i.e., high derivative) terms into the evolution equations, and this leads to severe stability constraints for explicit time-integration methods. Furthermore, the high order terms appear in non-local operators, making the application of implicit methods difficult. Our method uses the fundamental coefficients of the surface as dynamical variables, and employs a special isothermal parameterization of the interface which enables efficient application of implicit or linear propagator time-integration methods via a small-scale decomposition. The method is tested by computing the relaxation of an interface to a flat surface under the action of surface tension. These calculations employ an approximate interface velocity to test the stiffness reduction of the method. The approximate velocity has the same mathematical form as the exact velocity, but avoids the numerically intensive computation of the full Birkhoff-Rott integral. The algorithm is found to be effective at eliminating the severe time-step constraint that plagues explicit time-integration methods.

KW - 3D porous media flow

KW - Boundary integral method

KW - Stiff equations

KW - Surface tension

UR - http://www.scopus.com/inward/record.url?scp=84858441196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858441196&partnerID=8YFLogxK

U2 - 10.1016/j.matcom.2010.05.018

DO - 10.1016/j.matcom.2010.05.018

M3 - Article

AN - SCOPUS:84858441196

SN - 0378-4754

VL - 82

SP - 968

EP - 983

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

IS - 6

ER -