Review of preconditioning methods for fluid dynamics

A new computation procedure is developed for solving time-accurate, chemically reacting flows over a wide range of Mach numbers. The algorithm is based on scaling the pressure terms in the momentum equations and preconditioning the conservation equations to circumvent numerical difficulties at low Mach numbers. The resulting equations are solved using the lower-upper (LU) factorization method in a fully-coupled manner, with incorporation of a flux-differencing upwind TVD scheme to achieve high-order spatial accuracy. The transient behavior of the modeled system is preserved through implementation of the dual time-stepping integration technique. The capabilities of the scheme are illustrated by applying it to selected problems, including one-dimensional nozzle flows, two-dimensional channel flows, rocket-motor internal flows, and acoustic waves in a porous chamber with surface transpiration.

A Preconditioned Flux-Differencing Scheme for Chemically Reacting Flows at all Mach Numbers

: The extension of time-marching procedures to low Mach number and low Reynolds number conditions is considered. It is shown that the disparate speeds of the acoustic and particle waves prevents convergence at high Reynolds numbers while the requirement that both the Courant and the von Neumann numbers be of order one prevents convergence in very viscous flows. A perturbation expansion is used to introduce pseudo-acoustic waves that propagate at speeds similar to the particle speed at high Reynolds numbers and that allows both the inviscid and viscous time step parameters to be of order one at low Reynolds numbers. The resulting algorithm is shown to give convergence rates that are independent of either Mach number or Reynolds number over a range of five orders of magnitude in both parameters. Results are shown for strong heat addition in low speed flow encompassing this broad range of variables.

Computation of low-speed compressible flows with time-marching procedures

A perturbation expansion is used to obtain a system of conservation laws for compressible flows that is valid at arbitrarily low Mach numbers. These equations are rendered hyperbolic by adding an artificial time derivative to the energy equation, thus introducing pseudoacoustic waves with a speed the same order as the particle velocity. Traditional time-iterative schemes are shown to be effective in solving this system numerically. Stability calculations of the complete vector system indicate unconditional stability at all Mach numbers in the absence of gravity, but the source term introduced by buoyancy becomes destabilizing at Froude numbers below about 1. This instability is amplified by approximate factorization thus precluding solutions with gravity below this Mach number level. Computations of strong heat addition in low-Mach-number flow both with and without gravity confirm the stability predictions. Convergent solutions are maintained and are used to show the effect of gravity on such flowfields.

Computation of low-speed flow with heat addition

Impact of Source Terms on Reliability of CFD Algorithms

A numerical method for incompressible and compressible flow problems with smooth solutions

Hyperbolic systems with two different time-scales are considered, where the solutions vary on the slow scale only. For this type of problem semi-implicit difference methods are very natural, and in this paper we analyze the leap-frog backwards Euler scheme. In particular it is shown, that when the ratio $\varepsilon $ between the slow and the fast scale tends to zero, the solutions of the approximation converge to solutions of the reduced differential equation. Numerical experiments are included for illustration of the theoretical results.

A semi-implicit method for hyperbolic problems with different time-scales

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Jaime Guerra

Author Tools

Chat about Author

Papers

A numerical method for incompressible and compressible flow problems with smooth solutions

A semi-implicit method for hyperbolic problems with different time-scales