Numerical Simulation of Unsteady Nonisothermal Capillary Interfaces

A family of algorithms for simulation of unsteady nonisothermal capillary interfaces has been developed. The algorithms are based on a coordinate transformation method. The time-dependent unknown physical domain is mapped onto a rectangular computational domain, with the explicit form of the mapping function not being known. Four types of temporal discretization are used leading to the first-order accurate one-step implicit method, second-order accurate Crank–Nicolson and trapezoidal methods and second-order accurate two-step implicit method. In all cases, second-order finite-difference approximations were used for spatial discretizations. Various tests demonstrated that the algorithms deliver theoretically predicted accuracy, even for very large interfacial distortions. The Crank–Nicolson and trapezoidal methods have been found to be conditionally stable and thus are not recommended.