1,141 research outputs found
Asymptotic Preserving time-discretization of optimal control problems for the Goldstein-Taylor model
We consider the development of implicit-explicit time integration schemes for
optimal control problems governed by the Goldstein-Taylor model. In the
diffusive scaling this model is a hyperbolic approximation to the heat
equation. We investigate the relation of time integration schemes and the
formal Chapman-Enskog type limiting procedure. For the class of stiffly
accurate implicit-explicit Runge-Kutta methods (IMEX) the discrete optimality
system also provides a stable numerical method for optimal control problems
governed by the heat equation. Numerical examples illustrate the expected
behavior
Numerical simulation of two and three-dimensional viscous free surface flows in partially-filled containers using a surface capturing approach
A new surface capturing method is developed for numerically simulating viscous free surface flows in partially-filled containers. The method is based on the idea that the flow of two immiscible fluids (specifically, a liquid and a gas) within a closed container is governed by the equations of motion for a laminar, incompressible, viscous, nonhomogeneous (variable density) fluid. By computing the flowfields in both the liquid and gas regions in a consistent manner, the free surface can be captured as a discontinuity in the density field, thereby eliminating the need for special free surface tracking procedures;The numerical algorithm is developed using a conservative, implicit, finite volume discretization of the equations of motion. The algorithm incorporates the artificial compressibility method in conjunction with a dual time stepping strategy to maintain a divergence-free velocity field. A slope-limited, high order MUSCL scheme is adopted for approximating the inviscid flux terms, while the viscous fluxes are centrally differenced. Two different methods are considered for solving the resulting block-banded system of equations;The capabilities of the surface capturing method are demonstrated by calculating solutions to several challenging two and three-dimensional problems. The first test case, the two-dimensional broken dam problem, is considered in detail. Results are presented for several grid sizes, upwind schemes, and limiters, and are compared to experimental data from the literature. The solutions employing high order upwind interpolants and a compressive minmod limiter on the density are found to yield the best results. The two-dimensional, viscous Rayleigh-Taylor instability is examined next. Solutions for a density ratio of two are computed for various Reynolds numbers. Computed perturbation growth rates are shown to be in good agreement with theoretical predictions. Results for the three-dimensional broken dam problem are then presented. The computed free surface motions are found to be quite similar to the two-dimensional case. Finally, two cases involving axisymmetric spin-up in a spherical container are studied. The computed free surface shapes are found to exhibit the characteristic parabolic profiles as steady state conditions are approached
Efficient Reordered Nonlinear Gauss-Seidel Solvers With Higher Order For Black-Oil Models
The fully implicit method is the most commonly used approach to solve
black-oil problems in reservoir simulation. The method requires repeated
linearization of large nonlinear systems and produces ill-condi\-tioned linear
systems. We present a strategy to reduce computational time that relies on two
key ideas: (\textit{i}) a sequential formulation that decouples flow and
transport into separate subproblems, and (\textit{ii}) a highly efficient
Gauss--Seidel solver for the transport problems. This solver uses intercell
fluxes to reorder the grid cells according to their upstream neighbors, and
groups cells that are mutually dependent because of counter-current flow into
local clusters. The cells and local clusters can then be solved in sequence,
starting from the inflow and moving gradually downstream, since each new cell
or local cluster will only depend on upstream neighbors that have already been
computed. Altogether, this gives optimal localization and control of the
nonlinear solution process.
This method has been successfully applied to real-field problems using the
standard first-order finite volume discretization. Here, we extend the idea to
first-order dG methods on fully unstructured grids. We also demonstrate proof
of concept for the reordering idea by applying it to the full simulation model
of the Norne oil field, using a prototype variant of the open-source OPM Flow
simulator.Comment: Comput Geosci (2019
An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries
We review a scalable two- and three-dimensional computer code for
low-temperature plasma simulations in multi-material complex geometries. Our
approach is based on embedded boundary (EB) finite volume discretizations of
the minimal fluid-plasma model on adaptive Cartesian grids, extended to also
account for charging of insulating surfaces. We discuss the spatial and
temporal discretization methods, and show that the resulting overall method is
second order convergent, monotone, and conservative (for smooth solutions).
Weak scalability with parallel efficiencies over 70\% are demonstrated up to
8192 cores and more than one billion cells. We then demonstrate the use of
adaptive mesh refinement in multiple two- and three-dimensional simulation
examples at modest cores counts. The examples include two-dimensional
simulations of surface streamers along insulators with surface roughness; fully
three-dimensional simulations of filaments in experimentally realizable
pin-plane geometries, and three-dimensional simulations of positive plasma
discharges in multi-material complex geometries. The largest computational
example uses up to million mesh cells with billions of unknowns on
computing cores. Our use of computer-aided design (CAD) and constructive solid
geometry (CSG) combined with capabilities for parallel computing offers
possibilities for performing three-dimensional transient plasma-fluid
simulations, also in multi-material complex geometries at moderate pressures
and comparatively large scale.Comment: 40 pages, 21 figure
3D CFD analysis of an oil injected twin screw expander
Small scale Organic Rankine Cycle (ORC) systems have a big potential for waste heat recovery in the market. Due to the smaller volume flows inside these systems, non-conventional expansion technologies such as screw expanders become more interesting. Recent economic studies have shown the important role of screw machines in such cycles. However, in order to get a better understanding of the expansion behaviour in an ORC, appropriate simulation models of screw expanders are necessary. The flow inside an oil-injected twin screw expander is modeled in detail with 3D CFD (Computational Fluid Dynamics) calculations. These simulations are challenging because of the deforming domain and the narrow gaps between the screws or between a screw and the casing. The deforming mesh motion is handled by an in-house code which generates a block-structured grid with the help of the solutions of the Laplace problem. The oil-phase was modeled with an Eulerian multiphase model and the working fluid is treated compressible. The performance of the screw expander is strongly affected by the oil-injection which provides lubrication and a better sealing of the gaps. Therefore, the different types of leakages inside the screw expander are studied and monitored. As the result of the simulations, knowledge about the flow process and the losses inside the oil-injected screw expander is built up
- …