[PEM17-P03] Parameter tuning of a 5th order conservative and non-oscillatory scheme with super Gaussian distributions
Keywords:Advection equation, Vlasov simulation
Limiter functions used in the conservative and non-oscillatory scheme preserves the mass conservation and fulfills the non-oscillatory and positivity of plasma distribution functions with less computational cost for Vlasov simulations. The limiter functions have free parameters that control the gradient of the plasma distribution functions for numerical fluxes. The aim of this study is to optimize these parameters in order to achieve higher-accuracy without numerical oscillation and diffusion.
In previous study, we discussed the characteristics of two free parameters for tuning a 5th order conservative and non-oscillatory scheme with Gaussian distributions. The values of these parameters should be chosen to minimize the error between analytical and numerical fluxes. We found that the gradients in limiter functions are modified in the tail and not modified in the top and inflection point of the Gaussian distribution. The relational expression between these parameters was obtained in the tail.
In this study, we introduced super Gaussian distributions for changing the gradient in Gaussian distributions. The characteristics of the gradients are almost same as the previous results in the tail and inflection point. However, the gradients are modified in the top of super Gaussian distributions. We will optimize these parameters in limiter functions.
In previous study, we discussed the characteristics of two free parameters for tuning a 5th order conservative and non-oscillatory scheme with Gaussian distributions. The values of these parameters should be chosen to minimize the error between analytical and numerical fluxes. We found that the gradients in limiter functions are modified in the tail and not modified in the top and inflection point of the Gaussian distribution. The relational expression between these parameters was obtained in the tail.
In this study, we introduced super Gaussian distributions for changing the gradient in Gaussian distributions. The characteristics of the gradients are almost same as the previous results in the tail and inflection point. However, the gradients are modified in the top of super Gaussian distributions. We will optimize these parameters in limiter functions.