Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
The mimetic finite difference (MFD) methods mimic important properties of physical and mathematical models. As the result, conservation laws, solution symmetries, and the fundamental identities of the vector and tensor calculus are held for discrete models. The existing MFD methods for solving diffusion-type problems on arbitrary meshes are second-order accurate for the conservative variable (temperature, pressure, energy, etc.) and only first-order accurate for its flux. In many physical simulations such as reactive transport in porous media, compressible flows, etc., the flux accuracy makes significant impact on evolution of conservative quantities. We developed new high-order MFD methods which are second-order accurate for both conservative variable and its flux.
