A compact finite differences exact projection method for the Navier-Stokes equations on a staggered grid with fourth-order spatial precision

Autor(es)

Reis, G. A. ^[1] ; Tasso, I. V. M. ^[1] ; Souza, L. F. ^[1] ; Cuminato, J. A. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, ICMC, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMPUTERS & FLUIDS; v. 118, p. 19-31, SEP 2 2015.
• Citações Web of Science: 8

Resumo

An exact projection method for the numerical solution of the incompressible Navier-Stokes equations is devised. In all spatial discretizations, fourth-order compact finite differences are used, including domain boundaries and the Poisson equation that arises from the projection method. The integration in time is carried out by a second-order Adams Bashforth scheme. The discrete incompressibility constraint is imposed exactly (up to machine precision) by a simple and efficient discretization of the Poisson equation. Spatial and temporal accuracies, for both velocity and pressure, are verified through the use of analytical and manufactured solutions. The results show that the method converges with fourth-order accuracy in space and second-order accuracy in time, for both velocity and pressure. Additionally, two popular benchmark problems, the flow over a backward facing step and the lid-driven cavity flow, are used to demonstrate the robustness and correctness of the code. (C) 2015 Elsevier Ltd. All rights reserved. (AU)

• Processo FAPESP: 13/21501-8 - Modelagem computacional de alta resolução para fenômenos de corrente de turbidez em escala de campo
• Beneficiário: Italo Valença Mariotti Tasso
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 12/04471-5 - O método de interfaces imersas para a simulação de escoamentos com superfícies livres
• Beneficiário: Gabriela Aparecida dos Reis
• Modalidade de apoio: Bolsas no Brasil - Doutorado