AbstractChemically reacting flows have many applications in combustion. There are several difficulties in constructing high-order numerical methods: (1) Due to the rapid reaction rate, the system may contain stiff source terms. (2) The transition points near the shocks may trigger the stiff source leading to spurious shock speed. (3) Physically, the density, internal energy are positive, and th...
AbstractWe design and analyze some numerical methods for solving the Poisson-Nernst-Planck (PNP) equations. The numerical schemes, including finite difference method and discontinuous Galerkin method, respect three desired properties that are possessed by analytical solutions: I) conservation, II) positivity of solution, and III) free-energy dissipation. Advantages of different types of methods...
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