| Abstract: |
| Thermodynamically consistent models for any materials systems are the models that satisfy the conservation laws required by the physical systems and the thermodynamical laws for energy and entropy or equivalenetly by the Onsager principle for entropy production or energy dissipation. These models possess a special mathematical structure which can be exploited to yield energy stable schemes. This mathematical property of the models can also be exploited to produce positivity preserving schemes. Guided by the thermodynamical property, many nice numerical approximations can be developed to capture the physical properties of the underlying continuum models. We will present some strategies to render high order numerical schemes for such physical models. |
|