3,895 research outputs found
A WENO Algorithm of the Temperature and Ionization Profiles around a Point Source
We develop a numerical solver for radiative transfer problems based on the
weighted essentially nonoscillatory (WENO) scheme modified with anti-diffusive
flux corrections, in order to solve the temperature and ionization profiles
around a point source of photons in the reionization epoch. Algorithms for such
simulation must be able to handle the following two features: 1. the sharp
profiles of ionization and temperature at the ionizing front (I-front) and the
heating front (T-front), and 2. the fraction of neutral hydrogen within the
ionized sphere is extremely small due to the stiffness of the rate equations of
atom processes. The WENO scheme can properly handle these two features, as it
has been shown to have high order of accuracy and good convergence in capturing
discontinuities and complicated structures in fluid as well as to be
significantly superior over piecewise smooth solutions containing
discontinuities. With this algorithm, we show the time-dependence of the
preheated shell around a UV photon source. In the first stage the I-front and
T-front are coincident, and propagate with almost the speed of light. In later
stage, when the frequency spectrum of UV photons is hardened, the speeds of
propagation of the ionizing and heating fronts are both significantly less than
the speed of light, and the heating front is always beyond the ionizing front.
In the spherical shell between the I- and T-fronts, the IGM is heated, while
atoms keep almost neutral. The time scale of the preheated shell evolution is
dependent on the intensity of the photon source. We also find that the details
of the pre-heated shell and the distribution of neutral hydrogen remained in
the ionized sphere are actually sensitive to the parameters used. The WENO
algorithm can provide stable and robust solutions to study these details.Comment: 24 pages, 7 figures, accepted in New Astronom
HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation
Based on the multilevel interpolation theory, we constructed a meshless adaptive multiscale interpolation operator (MAMIO) with the radial basis function. Using this operator, any nonlinear partial differential equations such as Burgers equation can be discretized adaptively in physical spaces as a nonlinear matrix ordinary differential equation. In order to obtain the analytical solution of the system of ODEs, the homotopy analysis method (HAM) proposed by Shijun Liao was developed to solve the system of ODEs by combining the precise integration method (PIM) which can be employed to get the analytical solution of linear system of ODEs. The numerical experiences show that HAM is not sensitive to the time step, and so the arithmetic error is mainly derived from the discrete in physical space
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