Toward realistic simulations of magneto-thermal winds from weakly-ionized protoplanetary disks

Protoplanetary disks (PPDs) accrete onto their central T Tauri star via magnetic stresses. When the effect of ambipolar diffusion (AD) is included, and in the presence of a vertical magnetic field, the disk remains laminar between 1-5 au, and a magnetocentrifugal disk wind forms that provides an important mechanism for removing angular momentum. We present global MHD simulations of PPDs that include Ohmic resistivity and AD, where the time-dependent gas-phase electron and ion fractions are computed under FUV and X-ray ionization with a simplified recombination chemistry. To investigate whether the mass loading of the wind is potentially affected by the limited vertical extent of our existing simulations, we attempt to develop a model of a realistic disk atmosphere. To this end, by accounting for stellar irradiation and diffuse reprocessing of radiation, we aim at improving our models towards more realistic thermodynamic properties.Comment: 8 pages, 3 figures, ASTRONUM-2016 proceeding

Experimental Path-Following of Equilibria Using Newton’s Method, Part I:Theory, Modelling, Experiments

Modern numerical path-following techniques provide a comprehensive suite of computational tools to study the bifurcation behaviour of engineering structures. In contrast, experimental testing of load-bearing nonlinear structures is still performed using simple force control (dead loading) or displacement control (rigid loading). This means that established experimental methods cannot trace equilibrium manifolds in their entirety because structures snap to alternative equilibria at limit points in the forcing parameter and because branch switching to alternative equilibria cannot be controlled and performed reliably. To extend current testing methods, in Part I of this paper, we implement an experimental path-following method that uses tangent quantities (stiffness and residual forces) and Newton's method to continue along stable and unstable equilibrium paths and traverse limit points. In addition to enforcing the displacement at primary load-introduction points, the overall shape of the structure is controlled via secondary actuators and sensors. Small perturbations of the structure using the secondary actuators allow an experimental tangent stiffness to be computed, which is then used in a control algorithm. As a pertinent test case, the experimental method is applied to a transversely loaded shallow {circular} arch. Due to the complexity of the test setup, the experiment is first designed using a virtual testing environment based on a surrogate finite element model. Experimental results demonstrate the robustness of the proposed experimental method and the usefulness of virtual testing as a surrogate, but also highlight that experimental efficiency and the effects of noise and sensor uncertainty is of particular concern. In Part II, we present perspectives on future research directions and novel testing capabilities that are enabled by extending the methodology to pinpointing of critical points, tracing of critical boundaries, and branch switching

Continuation-minimization methods for stability problems

AbstractWe study the solution branches of stable and unstable bifurcations in certain semilinear elliptic eigenvalue problems with Dirichlet boundary conditions. A secant predictor-line search backtrack corrector continuation method is described to trace the solution curves numerically. Sample numerical results with computer graphic output are reported

Visualization of Load Security Region Bounded by Operational Constraints of Power Systems

This paper presents the method to visualize a set of feasible loading points, called “feasible regionâ€, in the two-dimensional power flow solution space. The visualization can be done by tracing the boundary of feasible region. The boundary points are determined by optimizing the reduced cost function with operational constraints. The method can also determine several kinds of feasible regions by assigning the appropriate free variables and its criteria. These feasible regions show the robustness of operating points and the limit of control actions. The six-bus test system illustrates the boundary tracing and impacts of system parameters on the shape of feasible region, i.e. the capacitor bank operation, load shedding, generator voltage controls, and load level

A novel Q-limit guided continuation power flow method for voltage stability analysis

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Voltage security assessment is becoming a more and more important issue due to the fact that electrical power systems are more prone to voltage instability under increased demand, and it can be time-consuming to determine the actual level of voltage security in large power systems. For this reason, this thesis presents a novel method for calculating the margin of voltage collapse that is based on the Continuation Power Flow (CPF) method. The method offers a flexible and reliable solution procedure without suffering from divergence problems even when near the bifurcation point. In addition, the new method accounts for reactive power limits. The algorithmic continuation steps are guided by the prediction of Q-limit breaking point. A Lagrange polynomial interpolation formula is used in this method in order to find the Q-limit breaking point indices that determine when the reactive power output of a generator has reached its limit. The algorithmic continuation steps will then be guided to the closest Q-limit breaking point, consequently reducing the number of continuation steps and saving computational time. The novel method is compared with alternative conventional and enhanced CPF methods. In order to improve CPF further, studies comparing the performance of using direct and iterative solvers in a power flow calculation have also been performed. I first attempt to employ the column approximate minimum degree (AMD) ordering scheme to reset the permutation of the coefficient matrix, which decreases the number of iterations required by iterative solvers. Finally, the novel method has been applied to a range of power system case studies including a 953 bus national grid transmission case study. The results are discussed in detail and compared against exiting CPF methods

Searching minima of an N-dimensional surface: A robust valley following method

AbstractA procedure is proposed to follow the “minimum path” of a hypersurface starting anywhere in the catchment region of the corresponding minimum. The method uses a modification of the so-called “following the reduced gradient” [1]. The original method connects points where the gradient has a constant direction. In the present letter, this is replaced by the successive directions of the tangent of the searched curve. The resulting pathway is that valley floor gradient extremal which belongs to the smallest (absolute) eigenvalue of the Hessian. The new method avoids third derivatives of the objective function. The effectiveness of the algorithm is demonstrated by using a polynomial test, the notorious Rosenbrock function in two, 20, and in 100 dimensions