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The PLIC/SN method that combines the second-order volume tracking method (PLIC-VOF) with the equation of surface normal (SN) vector was recently proposed (M. Sun, “Volume Tracking of Subgrid Particles,” International Journal for Numerical Methods in Fluids, Vol. 66, No. 12, 2011, pp. 1530-1554). The method is able to track the motion of a subgrid particle, but the accuracy is not as good as expected on high resolution grids for vortical flows. In this paper, a simple unsplit multidimensional advection algorithm is coupled with the equation of SN vector. The advection algorithm is formulated as the finite volume method, so that it can be used readily for both structured and unstructured grids while maintaining the exact mass conservation. The new method improves the accuracy significantly for high resolution grids. In the well-known test of the time-resolved vortex problem of T = 2, the circular interface is resolved with an accuracy better than ever using the equation of SN vector.
In this paper, several existence results of
multiple positive solutions are obtained for a boundary value problem with
p-Laplacian, by applying a fixed point theorem in cones. The interesting point
is that the nonlinear term f is involved with the first-order derivative explicitly.
Several classes of permutation polynomials
of the form
over finite fields are
presented in this paper, which is a further investigation on a recent work of
Li et al.