On propose un schema de differences finies pour l'equation de convection-diffusion a coefficients variables. Le systeme resultant peut etre resolu par des methodes iteratives

A single cell high order scheme for the convection-diffusion equation with variable coefficients

A study of finite difference approximations to steady-state, convection-dominated flow problems

High-order compact finite difference schemes for two-dimensional convection-diffusion-type differential equations with constant and variable convection coefficients are derived. The governing equations are employed to represent leading truncation terms, including cross-derivatives, making the overall O(h4) schemes conform to a 3 × 3 stencil. We show that the two-dimensional constant coefficient scheme collapses to the optimal scheme for the one-dimensional case wherein the finite difference equation yields nodally exact results. The two-dimensional schemes are tested against standard model problems, including a Navier-Stokes application. Results show that the two schemes are generally more accurate, on comparable grids, than O(h2) centred differencing and commonly used O(h) and O(h3) upwinding schemes.

Differential‐equation‐based representation of truncation errors for accurate numerical simulation

A control volume model of solute transport through a single fracture in a porous matrix is developed. Application to problems of contaminant transport through fractured clay demonstrates several strong features of the method. The control volume approach inherently conserves mass and treats dispersivity at interfaces in a physically correct manner. By employing an upstream weighting scheme, based on the exact solution to the one-dimensional steady state advection-dispersion equation, the model proves to be more efficient than previous single-fracture models. The significance of matrix diffusion in the direction parallel to the fracture axis is investigated. For the transport of a nonreactive tracer through a 20-micrometer-wide fracture in clay material, analytical solutions based on one-dimensional matrix diffusion are erroneous for flow velocities of less than 1 m/day. The influence of boundary conditions on two-dimensional matrix diffusion is considered, and the clean-up of a contaminated fracture is simulated.

A Control Volume Model of Solute Transport in a Single Fracture

Modeling turbulent recirculating flows by finite-volume methods—current status and future directions☆

Finite-difference and finite-element methods are widely used to solve problems described by sets of partial differential equations. However, the connections between the approximations made in the discretization process and the final solution errors, for a given grid, are often not clearly understood, especially when convection is a dominant factor. These connections are clarified in the present paper and, from the insight gained, a new method of formulating the discrete equations suggests itself. The results of applying two different schemes, that are both based on this method, to an example problem are presented. These are compared with results obtained using two finite-difference schemes. The new approach appears to hold considerable promise for future development.

Proposal for a new discrete method based on an assessment of discretization errors

Simulation of convection and diffusion processes by standard finite difference schemes and by influence schemes

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.

A. B. Strong

Author Tools

Chat about Author

Papers

Proposal for a new discrete method based on an assessment of discretization errors

Simulation of convection and diffusion processes by standard finite difference schemes and by influence schemes