scholarly journals Overview of the 2018 Workshop on Iterative Errors in Unsteady Flow Simulations

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
L. Eça ◽  
G. Vaz ◽  
M. Hoekstra ◽  
S. Pal ◽  
E. Muller ◽  
...  
Keyword(s):  
Unsteady Flow ◽  
Time Integration ◽  
Implicit Time ◽  
Test Case ◽  
Convergence Criteria ◽  
Courant Number ◽  
Time Step ◽  
Flow Solver ◽  
Flow Simulations ◽  
Implicit Time Integration

Abstract Two workshops were held at the ASME V&V Symposiums of 2017 and 2018 dedicated to Iterative Errors in Unsteady Flow Simulations. The focus was on the effect of iterative errors on numerical simulations performed with implicit time integration, which require the solution of a nonlinear set of equations at each time-step. The main goal of these workshops was to create awareness to the problem and to confirm that different flow solvers exhibited the same trends. The test case was a simple two-dimensional, laminar flow of a single-phase, incompressible, Newtonian fluid around a circular cylinder at the Reynolds number of 100. A set of geometrically similar multiblock structured grids was available and boundary conditions to perform the simulations were proposed to the participants. Results from seven flow solvers were submitted, but not all of them followed exactly the proposed conditions. One set of results was obtained with adaptive grid and time refinement using triangular elements (CADYF) and another used a compressible flow solver with a dual time stepping technique and a Mach number of 0.2 (DLR-Tau). The remaining five submissions were obtained with five different incompressible flow solvers (ansyscfx 14.5, pimplefoam, refresco, saturne, starccm+ v12.06.010-R8) using implicit time integration in the proposed grids. The results obtained in this simple test case showed that iterative errors may have a significant impact on the numerical accuracy of unsteady flow simulations performed with implicit time integration. Iterative errors can be significantly larger (one to two orders of magnitude) than the residuals and/or solution changes used as convergence criteria at each time-step. The Courant number affected the magnitude of the iterative errors obtained in the proposed exercise. For the same iterative convergence criteria at each time-step, increasing the Courant number tends to increase the iterative error.

Numerical Errors in Unsteady Flow Simulations

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
L. Eça ◽  
G. Vaz ◽  
S. L. Toxopeus ◽  
M. Hoekstra
Keyword(s):  
Statistical Convergence ◽  
Initial Condition ◽  
Convergence Criteria ◽  
Courant Number ◽  
Time Step ◽  
Flow Simulations ◽  
Numerical Errors ◽  
Data Points ◽  
Discretization Errors ◽  
Iterative Error

This article discusses numerical errors in unsteady flow simulations, which may include round-off, statistical, iterative, and time and space discretization errors. The estimation of iterative and discretization errors and the influence of the initial condition on unsteady flows that become periodic are discussed. In this latter case, the goal is to determine the simulation time required to reduce the influence of the initial condition to negligible levels. Two one-dimensional, unsteady manufactured solutions are used to illustrate the interference between the different types of numerical errors. One solution is periodic and the other includes a transient region before it reaches a steady-state. The results show that for a selected grid and time-step, statistical convergence of the periodic solution may be achieved at significant lower error levels than those of iterative and discretization errors. However, statistical convergence deteriorates when iterative convergence criteria become less demanding, grids are refined, and Courant number increased.For statistically converged solutions of the periodic flow and for the transient solution, iterative convergence criteria required to obtain a negligible influence of the iterative error when compared to the discretization error are more strict than typical values found in the open literature. More demanding criteria are required when the grid is refined and/or the Courant number is increased. When the numerical error is dominated by the iterative error, it is pointless to refine the grid and/or reduce the time-step. For solutions with a numerical error dominated by the discretization error, three different techniques are applied to illustrate how the discretization uncertainty can be estimated, using grid/time refinement studies: three data points at a fixed Courant number; five data points involving three time steps for the same grid and three grids for the same time-step; five data points including at least two grids and two time steps. The latter two techniques distinguish between space and time convergence, whereas the first one combines the effect of the two discretization errors.

scholarly journals Performance of Composite Implicit Time Integration Scheme for Nonlinear Dynamic Analysis

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
William Taylor Matias Silva ◽  
Luciano Mendes Bezerra
Keyword(s):  
Transient Response ◽  
Time Integration ◽  
Nonlinear Dynamic Analysis ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Structural Dynamic ◽  
Implicit Time Integration ◽  
Time Integration Scheme

This paper presents a simple implicit time integration scheme for transient response solution of structures under large deformations and long-time durations. The authors focus on a practical method using implicit time integration scheme applied to structural dynamic analyses in which the widely used Newmark time integration procedure is unstable, and not energy-momentum conserving. In this integration scheme, the time step is divided in two substeps. For too large time steps, the method is stable but shows excessive numerical dissipation. The influence of different substep sizes on the numerical dissipation of the method is studied throughout three practical examples. The method shows good performance and may be considered good for nonlinear transient response of structures.

scholarly journals Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration

2018 ◽  
Vol 77 (2) ◽  
pp. 819-849 ◽  
Author(s):  
Debojyoti Ghosh ◽  
Mikhail A. Dorf ◽  
Milo R. Dorr ◽  
Jeffrey A. F. Hittinger
Keyword(s):  
Time Integration ◽  
Implicit Time ◽  
Magnetized Plasmas ◽  
Kinetic Simulation ◽  
Implicit Time Integration

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

An Explicit-Implicit Time Integration Approach for Finite Element Evaluation of Engine Load Following an FBO Event

2017 ◽  
Author(s):  
Yiliu Weng ◽  
Lipeng Zheng
Keyword(s):  
Finite Element ◽  
Extreme Event ◽  
Time Integration ◽  
Implicit Time ◽  
Engine Load ◽  
Load Following ◽  
Fine Mesh ◽  
Implicit Time Integration ◽  
Integration Approach ◽  
Fan Blade

Engine fan blade-off (FBO) is an extreme event that could well place the flight safety at risk. When it happens, the engine will experience high-velocity impact at first, and then enter into a “high-power” stage due to huge unbalance before coming to a steady state called “windmilling”. The analytical process for FBO can be split into two phases, one for impact simulation and the other for obtaining the FBO load to pylon. Typically, explicit method with fine mesh finite elements is used in the first phase, and implicit method with coarse meshes is adopted in the second one. In most cases, the only connection between these two analyses may be the unbalance level caused by FBO. More structural responses other than the unbalance level due to fan blade impact are actually ignored in the succeeding implicit analysis. Attempts have been made by Boeing, GE and MSC to integrate these two processes by adding some features in MD Nastran. Yet the intermediate binary files created and the restricted input entries make the integration process quite inflexible. This paper introduces an explicit-implicit time integration approach for finite element analysis of engine load following an FBO event. The proposed method attempts to connect the two stages more closely, yet in a more flexible manner. In this approach, the engine structural response under FBO obtained from explicit analysis is transferred to the implicit analysis, together with the unbalance level caused by blade loss. The necessity of the approach is discussed, and sensitivity analysis is conducted to understand the factors that play significant roles in the approach. As the models for explicit and implicit analyses are different in mesh sizes and scales, the authors also develop a tool that can interpolate the load information and further, smooth it to fit calculation. Finally, the approach is tested on a full engine model to show its applicability and advantages over the traditional method for load evaluation of FBO event.

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