Reduced modeling of MHD instabilities

Summary form only given. Mathematical models of plasma instabilities, such as dense z-pinches, are often described by systems of nonlinear PDEs, which involve numerous uncertainties in equation parameters, boundary and initial conditions. Instabilities and high dimension of these models may amplify uncertainties and result in unpredictable simulations, which mirrors the unpredictability of real systems. This has two important aspects: one is that underlying dynamics may exhibit extreme sensitivity to the variation of their parameters, initial and boundary conditions, which has been studied in the context of bifurcation phenomena and deterministic chaos; the second is the combinatorial complexity of evaluating all model combinations that arise from possible variations in assumptions, parameters and initial data which prohibits direct evaluation of model uncertainties. Thus, it is important to understand and quantify the limits of predictability for full system simulation in terms of the uncertainties; inherent structure of the model and its components; the length of the observation interval; and to develop computational approaches minimizing the effect of uncertainties and reducing simulation time while preserving and controlling the accuracy of obtained results. In this paper we outline a computational approach leading to the derivation of a hierarchy of reduced models of initial complex systems. Each of these simplified models intend to provide a certain degree of inner averaging for individual elaborated simulations of the initial system and present more robust and practically significant results than individual computation events. Evaluation of simplified models significantly reduces simulation time and lead to more accurate and profound classification of complex unstable phenomena.