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Full-Text Articles in Physical Sciences and Mathematics
Arbitrarily High-Order Unconditionally Energy Stable Schemes For Thermodynamically Consistent Gradient Flow Models, Yuezheng Gong, Jia Zhao, Qi Wang
Arbitrarily High-Order Unconditionally Energy Stable Schemes For Thermodynamically Consistent Gradient Flow Models, Yuezheng Gong, Jia Zhao, Qi Wang
Mathematics and Statistics Faculty Publications
We present a systematic approach to developing arbitrarily high-order, unconditionally energy stable numerical schemes for thermodynamically consistent gradient flow models that satisfy energy dissipation laws. Utilizing the energy quadratization method, we formulate the gradient flow model into an equivalent form with a corresponding quadratic free energy functional. Based on the equivalent form with a quadratic energy, we propose two classes of energy stable numerical approximations. In the first approach, we use a prediction-correction strategy to improve the accuracy of linear numerical schemes. In the second approach, we adopt the Gaussian collocation method to discretize the equivalent form with a quadratic …
Fully Discrete Second-Order Linear Schemes For Hydrodynamic Phase Field Models Of Binary Viscous Fluid Flows With Variable Densities, Yuezheng Gong, Jia Zhao, Xiaogang Yang, Qi Wang
Fully Discrete Second-Order Linear Schemes For Hydrodynamic Phase Field Models Of Binary Viscous Fluid Flows With Variable Densities, Yuezheng Gong, Jia Zhao, Xiaogang Yang, Qi Wang
Mathematics and Statistics Faculty Publications
We develop spatial-temporally second-order, energy stable numerical schemes for two classes of hydrodynamic phase field models of binary viscous fluid mixtures of different densities. One is quasi-incompressible while the other is incompressible. We introduce a novel energy quadratization technique to arrive at fully discrete linear schemes, where in each time step only a linear system needs to be solved. These schemes are then shown to be unconditionally energy stable rigorously subject to periodic boundary conditions so that a large time step is plausible. Both spatial and temporal mesh refinements are conducted to illustrate the second-order accuracy of the schemes. The …