Adaptive Hierarchical Coupling of Kinetic and Fluid Plasma Models on hybrid GPU-CPU systems

Simon Lautenbach, Thomas Trost, Rainer Grauer

sl@tp1.rub.de, grauer@tp1.rub.de

Physical Context

Vlasov Model

\({ \partial_t f_s(\mathbf x,\mathbf v, t) + \mathbf{v}\cdot \nabla_{\mathbf{x}}f_s + \frac{q_s}{m_s}\big(\mathbf{E} + \mathbf{v} \times \mathbf{B} \big)\cdot \nabla_{\mathbf{v}}f_s = 0 }\\\)

Solved with semi-lagrangian PFC scheme (Filbet et al. (2001)):

Solved on GPUs

Fluid Model (10 Moments)

\begin{align*} \partial_t n_s &= - \nabla \cdot (n_s\mathbf{u}_s) \\ \partial_t (m_sn_s\mathbf{u}_s) &= - \nabla\cdot(2\mathbb{E}_s) + q_sn_s \big( \mathbf E + \mathbf{u}_s \times \mathbf B \big) \\ \partial_t \mathbb{E}_s &= -\nabla\cdot\Big( 3\operatorname{sym}(\mathbb{E}_s\mathbf{u}_s) - m_sn_s\mathbf{u}_s\mathbf{u}_s\mathbf{u}_s\Big)\\ &\phantom{=\ } + q_s \operatorname{sym}\left(n_s\mathbf{u}_s \mathbf E + \frac{2}{m_s}\mathbb{E}_s\times \mathbf B\right) - {\color{red}{\nabla \cdot \mathbb{Q}_s}}\\ \end{align*}

Closure (Wang et al. (2015)): \({ {\color{red}{\nabla \cdot \mathbb{Q}_s}} = \frac{1}{\sqrt{2}}v_{\text{th},s}|k_0|(\mathbb{P}_s - p_s\mathbb 1) }\)

Solved with CWENO