Specification of PSIDE

PSIDE is a code for solving implicit differential equations on parallel computers. It is an implementation of the four-stage Radau IIA method. The nonlinear systems are solved by a modified Newton process, in which every Newton iterate itself is computed by an iteration process. This process is constructed such that the four stage values can be computed simultaneously. We describe here how PSIDE is set up as a modular system and what control strategies have been chosen

Stochastic and Statistical Methods in Climate, Atmosphere, and Ocean Science

Introduction The behavior of the atmosphere, oceans, and climate is intrinsically uncertain. The basic physical principles that govern atmospheric and oceanic flows are well known, for example, the Navier-Stokes equations for fluid flow, thermodynamic properties of moist air, and the effects of density stratification and Coriolis force. Notwithstanding, there are major sources of randomness and uncertainty that prevent perfect prediction and complete understanding of these flows. The climate system involves a wide spectrum of space and time scales due to processes occurring on the order of microns and milliseconds such as the formation of cloud and rain droplets to global phenomena involving annual and decadal oscillations such as the EL Nio-Southern Oscillation (ENSO) and the Pacific Decadal Oscillation (PDO) [5]. Moreover, climate records display a spectral variability ranging from 1 cycle per month to 1 cycle per 100, 000 years [23]. The complexity of the climate system stems in large part from the inherent nonlinearities of fluid mechanics and the phase changes of water substances. The atmosphere and oceans are turbulent, nonlinear systems that display chaotic behavior (e.g., [39]). The time evolutions of the same chaotic system starting from two slightly different initial states diverge exponentially fast, so that chaotic systems are marked by limited predictability. Beyond the so-called predictability horizon (on the order of 10 days for the atmosphere), initial state uncertainties (e.g., due to imperfect observations) have grown to the point that straightforward forecasts are no longer useful. Another major source of uncertainty stems from the fact that numerical models for atmospheric and oceanic flows cannot describe all relevant physical processes at once. These models are in essence discretized partial differential equations (PDEs), and the derivation of suitable PDEs (e.g., the so-called primitive equations) from more general ones that are less convenient for computation (e.g., the full Navier-Stokes equations) involves approximations and simplifications that introduce errors in the equations. Furthermore, as a result of spatial discretization of the PDEs, numerical models have finite resolution so that small-scale processes with length scales below the model grid scale are not resolved. These limitations are unavoidable, leading to model error and uncertainty. The uncertainties due to chaotic behavior and unresolved processes motivate the use of stochastic and statistical methods for modeling and understanding climate, atmosphere, and oceans. Models can be augmented with random elements in order to represent time-evolving uncertainties, leading to stochastic models. Weather forecasts and climate predictions are increasingly expressed in probabilistic terms, making explicit the margins of uncertainty inherent to any prediction

Adaptive Time Stepping for Transient Network Flow Simulation in Rocket Propulsion Systems

Fluid and thermal transients found in rocket propulsion systems such as propellant feedline system is a complex process involving fast phases followed by slow phases. Therefore their time accurate computation requires use of short time step initially followed by the use of much larger time step. Yet there are instances that involve fast-slow-fast phases. In this paper, we present a feedback control based adaptive time stepping algorithm, and discuss its use in network flow simulation of fluid and thermal transients. The time step is automatically controlled during the simulation by monitoring changes in certain key variables and by feedback. In order to demonstrate the viability of time adaptivity for engineering problems, we applied it to simulate water hammer and cryogenic chill down in pipelines. Our comparison and validation demonstrate the accuracy and efficiency of this adaptive strategy

On diffuse interface modeling and simulation of surfactants in two-phase fluid flow

An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow

A Control Perspective to Adaptive Time Stepping in Reservoir Simulation

Reservoir modelling is an important tool in the management of hydrocarbon reservoirs. In fact, reservoir models are often a cost effective and time efficient alternative to a trial-and- error field management approach. Reservoir models allow oil companies to simulate various reservoir conditions and management strategies without having to spend considerable amount of money and time. Consequently, it is crucial to find ways to generate fast and accurate reservoir models to assist in making these crucial decisions. Within a reservoir simulator, the time discretization scheme is one of the most sensitive and computer intensive steps of the entire simulator. As a result, it is vital to find an efficient ways to perform this step in order to optimize the performance of the simulator. During the time discretization process, the choice of the time-step is a crucial decision. In fact, the time-step affects the computation time, the convergence, the accuracy and the amount of memory space used by the computer to run the simulation. We have to pick a time-step that is small enough to allow the solution to converge, but also sufficiently large to avoid high computation times. In order to tackle this problem, there are several adaptive time-stepping methods developed to automatically adjust the time-step and make sure that it remains within an optimal range. In this study, we investigate the effectiveness of using the Proportional-Integral-Derivative controller (PID) to regulate the error and the variations in pressure and saturation during the simulation of a reservoir system. We compare the performance of the PID controller with the basic controller conventionally used in adaptive time-stepping. The results show that PID algorithm used to control the variations in pressure and saturation can be more efficient than the basic controller as long as the proper PID coefficients are used in the simulation. We were able to reduce the computation cost with the use of the PID controller while maintaining the same level of accuracy as the basic method. The manual tuning of the controller can be time-consuming and future would have to include automatic tuning algorithms specifically tailored for adaptive time-stepping purposes. Otherwise, the benefit associated with using the PID controller would be dwarfed by the time-consuming manual tuning process. We also tested the PID controller to regulate the error within the Newton-Raphson loop. The results showed that the use of the PID controller inside this loop results in instabilities that cause the reservoir simulator to run inefficiently