TY - JOUR
T1 - The Immersed Interface Method for Simulating Two-Fluid Flows
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 447
EP - 472
PY - 2014
DA - 2014/07
SN - 7
DO - http://doi.org/10.4208/nmtma.2014.1309si
UR - https://global-sci.org/intro/article_detail/nmtma/5884.html
KW - Immersed interface method, two-fluid flows, jump conditions, augmented variable
approach, singular force, Cartesian grid methods.
AB - <p style="text-align: justify;">We develop the immersed interface method (IIM) to simulate a two-fluid flow of two immiscible fluids
with different density and viscosity. Due to the surface tension and the discontinuous fluid properties,
the two-fluid flow has nonsmooth velocity and discontinuous pressure across the moving sharp interface
separating the two fluids. The IIM computes the flow on a fixed Cartesian grid by incorporating
into numerical schemes the necessary jump conditions induced by the interface.
We present how to compute these necessary jump conditions from the analytical principal jump
conditions derived in [Xu, DCDS, Supplement 2009, pp. 838-845]. We test our method on some canonical
two-fluid flows. The results demonstrate that the method can handle large density and viscosity ratios,
is second-order accurate in the infinity norm, and conserves mass inside a closed interface.</p>