The Experts below are selected from a list of 3585 Experts worldwide ranked by ideXlab platform

Rachel Jorgensen - One of the best experts on this subject based on the ideXlab platform.

Ellie Campbell - One of the best experts on this subject based on the ideXlab platform.

Samet Tatar - One of the best experts on this subject based on the ideXlab platform.

Ping Lin - One of the best experts on this subject based on the ideXlab platform.

  • Energy Law preserving c0 finite element schemes for phase field models in two phase flow computations
    Journal of Computational Physics, 2011
    Co-Authors: Jinsong Hua, Ping Lin, Chun Liu, Qi Wang
    Abstract:

    We use the idea in [33] to develop the Energy Law preserving method and compute the diffusive interface (phase-field) models of Allen-Cahn and Cahn-Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C^0 finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete Energy Law can still be derived for these diffusive interface models. Through an example we demonstrate that the Energy Law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the Energy Law preserving method to the model of Cahn-Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method.

  • an Energy Law preserving c0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics
    Journal of Computational Physics, 2007
    Co-Authors: Ping Lin, Chun Liu, Hui Zhang
    Abstract:

    In this paper, we use finite element methods to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain @W. We reformulate the original model in the weak form which is consistent with the continuous dissipative Energy Law for the flow and director fields in W^1^,^2^+^@s(@W) (@s>0 is an arbitrarily small number). This enables us to use convenient conformal C^0 finite elements in solving the problem. Moreover, a discrete Energy Law is derived for a modified midpoint time discretization scheme. A fixed iterative method is used to solve the resulted nonlinear system so that a matrix free time evolution may be achieved and velocity and director variables may be solved separately. A number of hydrodynamical liquid crystal examples are computed to demonstrate the effects of the parameters and the performance of the method.

Richard Todd - One of the best experts on this subject based on the ideXlab platform.