Numerical Method for Eulerian Vlasov Simulation Based on Multi-Moment Scheme∗)

A new scheme referred to as the multi-moment (MM) scheme is explored to develop a more reliable Vlasov code from the viewpoint of numerical properties. The MM scheme is based on the Eulerian approach, where spatial derivatives are evaluated by interpolation functions locally constructed by not only grid values but also 0th-, 1st-, and 2nd-order moment values between grids, which largely increases numerical accuracy and resolution. Through the Fourier analyses and benchmark tests of one-dimensional (1D) and 2D transport simulations, it is found that the MM scheme exhibits significantly smaller numerical dissipation and dispersion even near the Nyquist wave-number, and as a result, the MM scheme decreases the numerical cost. The MM scheme is also applied to a 1D Vlasov-Poisson simulation and we find that the scheme captures finer scale structure in velocity space compared to the conservative form of interpolated differential operator (IDO-CF) scheme, while also maintaining good energy conservation.