Fast Solvers for Unsteady Thermal Fluid Structure Interaction

We consider time dependent thermal fluid structure interaction. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet-Neumann method and a fixed point iteration is employed. As a refence solver a previously developed efficient time adaptive higher order time integration scheme is used. To improve upon this, we work on reducing the number of fixed point coupling iterations. Thus, first widely used vector extrapolation methods for convergence acceleration of the fixed point iteration are tested. In particular, Aitken relaxation, minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are considered. Second, we explore the idea of extrapolation based on data given from the time integration and derive such methods for SDIRK2. While the vector extrapolation methods have no beneficial effects, the extrapolation methods allow to reduce the number of fixed point iterations further by up to a factor of two with linear extrapolation performing better than quadratic.Comment: 17 page

Neural network interpretation of electromagnetic ellipticity data in a frequency range from 1 kHz to 32 MHz

A new real-time in-field interpretation and visualization scheme and software, using neural networks for the detection and localization of buried waste, and the boundaries of waste sites, has been developed. The capabilities and limitations of the high-frequency (1 kHz to 1 MHz and 31 kHz to 32 MHz) electromagnetic ellipticity systems are analyzed by numerically studying the sensitivity of the acquired 3D-ellipticity to model parameters describing the geometry of the systems and the electrical parameters of layered-earth models. Changes in ellipticity due to coil misalignment in standard operating mode are typically just 1% to 2%. Changes due to variations in layered-earth model parameters (resistivity, relative dielectric constant, and thickness) are typically at least one order of magnitude higher. Hence, it will be possible to resolve these parameters. For conductive models (resistivity < 50 Ωm) it will be hard to determine the relative dielectric constant and for models with high relative dielectric constants it will be hard to determine the resistivity, especially if it is greater than 1000 Ωm. The results of the sensitivity analysis contribute considerably to the training of several neural networks to determine the electrical properties of the subsurface. The two classes of artificial neural network paradigms utilized in this study are the radial basis function and the modular neural network algorithms. One-dimensional layered-earth inversions are performed by neural networks using ellipticity data. The three-dimensional localization of metallic objects (e.g. drums) is done by visualizing the results of one particular halfspace neural network technique. Several small conductive objects have been detected by applying this technique to data collected in controlled physical modeling field experiments. Classification neural networks are trained on field data to categorize ellipticity soundings into either a target or a background class. Two environmental geophysics field case studies were analyzed using the developed interpretation system and the visualization software. The first case study involves mapping subsidence areas caused by an underground coal mine fire in Wyoming. The neural network interpretations from the mine survey match comparable inversion results. The second study documents the successful characterization of a simulated hazardous waste pit at the Idaho National Engineering Laboratory

Dissipation of upwind schemes at high wave numbers

A modification of the Roe scheme aimed at low Mach number flows is discussed. It improves the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. No conflict is observed between the reduced dissipation and the accuracy or stability of the scheme in any of the investigated test cases ranging from low Mach number potential flow to hypersonic viscous flow around a cylinder

A new domain‐based implicit‐explicit time stepping scheme based on the class of exponential integrators called sEPIRK

Reliable simulations of flows in real applications involve the task of discretizing both space and time in an accurate and efficient way. To cope with the large semidiscrete systems resulting from a space discretization on appropriate grids, which often include comparatively few very small cells near solid walls for boundary layer resolution, an implicit-explicit time stepping scheme can be the most efficient variant. We present such a type of scheme utilizing recent exponential integrators called sEPIRK and show its computational advantages opposed to IMEX-Runge-Kutta schemes

Adopting (s)EPIRK schemes in a domain-based IMEX setting

The simulation of viscous, compressible flows around complex geometries or similar applications often inherit the task of solving large, stiff systems of ODEs. Domain-based implicit-explicit (IMEX) type schemes offer the possibility to apply two different schemes to different parts of the computational domain. The goal hereby is to decrease the computational cost by increasing the admissible step sizes with no loss of stability and by reducing the system sizes of the linear solver within the implicit integrator. But which combination of methods reaches the largest gain in efficiency? Coupling of Runge-Kutta methods or different multistep methods has been investigated so far by other authors. Here, we inspect the adoption of the recently introduced exponential integrators called EPIRK and sEPIRK in the IMEX setting, since they are perfectly suited for large, stiff systems of ODEs

Extrapolation in Time in Thermal Fluid Structure Interaction

We consider time dependent thermal fluid structure interaction. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet-Neumann method and a fixed point iteration is employed. As a reference solver a previously developed efficient time adaptive higher order time integration scheme is used. To improve upon this, we work on reducing the number of fixed point coupling iterations. Thus, we explore the idea of extrapolation based on data given from the time integration and derive such methods for SDIRK2. This allows to reduce the number of fixed point iterations further by up to a factor of two with linear extrapolation performing better than quadratic

Efficient Time Integration of IMEX Type using Exponential Integrators for Compressible, Viscous Flow Simulation

We investigate the adaption of the recently developed exponential integrators called EPIRK in the so-called domain-based implicit-explicit (IMEX) setting of spatially discretized PDE's. The EPIRK schemes were shown to be efficient for sufficiently stiff problems and offer high precision and good stability properties like A- and L-stability in theory. In practice, however, we can show that these stability properties are dependent on the parameters of the interior approximation techniques.Here, we introduce the IMEX-EPIRK method, which consists of coupling an explicit Runge-Kutta scheme with an EPIRK scheme. We briefly analyze its linear stability, show its conservation property and set up a CFL condition. Though the method is convergent of only first order, it demonstrates the advantages of this novel type of schemes for stiff problems very well

On stability and conservation properties of (S)epirk integrators in the context of discretized pdes

Exponential integrators are becoming increasingly popular for stiff problems of high dimension due to their attractive property of solving the linear part of the system exactly and hence being A-stable. In practice, however, exponential integrators are implemented using approximation techniques to matrix-vector products involving functions of the matrix exponential (the so-called ϕ-functions) to make them efficient and competitive to other state-of-the-art schemes. We will examine linear stability and provide a Courant–Friedrichs–Lewy (CFL) condition of special classes of exponential integrator schemes called EPIRK and sEPIRK and demonstrate their dependence on the parameters of the embedded approximation technique. Furthermore, a conservation property of the EPIRK schemes is proven