| Abstract: |
| I will presents a general numerical platform for designing accurate, efficient, and stable numerical algorithms for incompressible hydrodynamic models that obey thermodynamical laws. The obtained numerical schemes are automatically linear in time. It decouples the hydrodynamic variable and other state variables such that only small-size linear problems need to be solved at each time marching step. Furthermore, if the classical velocity projection method is utilized, the velocity field and pressure field can be decoupled. In the end, only a few elliptic-type equations shall be solved in each time step. Several benchmark numerical examples are presented to further illustrate the proposed numerical framework`s accuracy, stability, and efficiency. |
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