Multigrid Convergence Rates of a Sequential and a Parallel Navier-Stokes Solver

1995 ◽  
pp. 251-262 ◽  
Author(s):  
Friedhelm Schieweck
Keyword(s):  
Convergence Rates ◽  
Navier Stokes ◽  
Multigrid Convergence

scholarly journals Optimal Lp–Lq convergence rates for the compressible Navier–Stokes equations with potential force

2007 ◽  
Vol 238 (1) ◽  
pp. 220-233 ◽  
Author(s):  
Renjun Duan ◽  
Hongxia Liu ◽  
Seiji Ukai ◽  
Tong Yang
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Potential Force ◽  
Navier Stokes Equations

Richardson Extrapolation-Based Discretization Uncertainty Estimation for Computational Fluid Dynamics

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Tyrone S. Phillips ◽  
Christopher J. Roy
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Convergence Rates ◽  
Richardson Extrapolation ◽  
Local Solution ◽  
Navier Stokes ◽  
Grid Convergence ◽  
Computational Fluid Dynamics Cfd ◽  
Grid Convergence Index ◽  
2D And 3D

This study investigates the accuracy of various Richardson extrapolation-based discretization error and uncertainty estimators for problems in computational fluid dynamics (CFD). Richardson extrapolation uses two solutions on systematically refined grids to estimate the exact solution to the partial differential equations (PDEs) and is accurate only in the asymptotic range (i.e., when the grids are sufficiently fine). The uncertainty estimators investigated are variations of the grid convergence index and include a globally averaged observed order of accuracy, the factor of safety method, the correction factor method, and least-squares methods. Several 2D and 3D applications to the Euler, Navier–Stokes, and Reynolds-Averaged Navier–Stokes (RANS) with exact solutions and a 2D turbulent flat plate with a numerical benchmark are used to evaluate the uncertainty estimators. Local solution quantities (e.g., density, velocity, and pressure) have much slower grid convergence on coarser meshes than global quantities, resulting in nonasymptotic solutions and inaccurate Richardson extrapolation error estimates; however, an uncertainty estimate may still be required. The uncertainty estimators are applied to local solution quantities to evaluate accuracy for all possible types of convergence rates. Extensions were added where necessary for treatment of cases where the local convergence rate is oscillatory or divergent. The conservativeness and effectivity of the discretization uncertainty estimators are used to assess the relative merits of the different approaches.

scholarly journals COMPUTATIONAL OPTIMIZATION FOR INTEGRAL TRANSFORM ALGORITHMS APPLIED TO THE LID-DRIVEN CAVITY FLOW PROBLEM

2007 ◽  
Vol 6 (1) ◽  
pp. 104
Author(s):  
J. M. B. S. Guigon ◽  
J. S. Pérez Guerrero ◽  
R. M. Cotta
Keyword(s):  
Error Control ◽  
Convergence Rates ◽  
Flow Problem ◽  
Stokes Equations ◽  
Integral Transform ◽  
Cavity Flow ◽  
Navier Stokes ◽  
Computational Optimization ◽  
Aspect Ratios ◽  
Computational Performance

An analysis is presented of the computational optimization for integral transform algorithms using the streamfunction only formulation of the Navier-Stokes equations, as applied to the steady incompressible laminar flow of a Newtonian fluid in two-dimensional formulation. The classical lid-driven rectangular cavity flow problem is considered in order to revise the conventional development of the Generalized Integral Transform Technique (GITT). The GITT is applied transforming the partial differential equation into a system of coupled ordinary differential equations, which is numerically solved by a general algorithm for boundary value problems, using a subroutine from the IMSL library with automatic error control. The conventional algorithm written in FORTRAN language is modified and tested seeking its optimization. A few different strategies of applying the technique are considered to achieve improved computational performance and allowing the inspection of convergence rates in the eigenfunction expansion of the original potentials for high Reynolds numbers. These different algorithm alternatives are analyzed and the relative merits are discussed. Results for different values of the Reynolds number and cavity aspect ratios are presented in tabular and graphical forms and fully converged results are critically compared against previously published findings.

Simultaneous Variable Solutions of the Incompressible Steady Navier-Stokes Equations in General Curvilinear Coordinate Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 299-305 ◽  
Author(s):  
G. Vradis ◽  
V. Zalak ◽  
J. Bentson
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Flow Direction ◽  
Solution Algorithm ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Solution Technique ◽  
Algebraic Equations ◽  
Coordinate Systems ◽  
Navier Stokes Equations

A simultaneous variable solution technique for the incompressible, steady, two-dimensional Navier-Stokes equations in primitive formulation and general curvilinear orthogonal and nonorthogonal coordinate systems has been developed. The governing equations are discretized using finite difference approximations. The formulation is fully second order accurate and the well-known staggered grid of Welch and Harlow is used. The solution algorithm is based on an iterative marching technique in which the algebraic equations are linearized by evaluating the coefficients at the previous iteration level. The resulting system of linear equations is solved in a marching fashion by employing a block tridiagonal solution algorithm to obtain the solution along lines transverse to the main flow direction. The strong pressure-velocity coupling inherent in the present formulation results in high convergence rates. Flows in channels of different geometries have been computed and the results have been compared to available data in the literature. In all cases the method has demonstrated to be accurate, robust and computationally efficient.

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