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The adaptive generalized Riemann problem (GRP) scheme for 2–D compressible fluid flows has been proposed in [25, Han, Li and Tang, An adaptive GRP scheme for compressible fluid flows, and it displays the capability in overcoming difficulties such as the start-up error for a single shock, and the numerical instability of the almost stationary shock. In this(More)
This paper presents an adaptive mesh redistribution (AMR) method for solving the nonlinear Hamilton-Jacobi equations and level set equations in two-and three-dimensions. Our approach includes two key ingredients: a non-conservative second-order interpolation on the updated adaptive grids, and a class of monitor functions (or indicators) suitable for the(More)
Image charge approximations are developed for electric potentials in the Poisson-Boltzmann theory in inhomogeneous media consisting of dielectrics or electrolyte solutions such as the layered structure in a membrane or cylindrical ion-channels. The image charges are obtained either by a least square fitting between the potential of unknown images and the(More)