Convergence Of Finite Volume Method Research Articles

Convergence and error estimates of a penalization finite volume method for the compressible Navier–Stokes system

Abstract In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently, in order to study convergence and error estimates of a numerical method domain-related discretization errors, the so-called variational crimes, need to be taken into account. In this paper we apply the penalty approach to control domain-related discretization errors. We embed the physical domain into a large enough cubed domain and study the convergence of a finite volume method for the corresponding domain-penalized problem. We show that numerical solutions of the penalized problem converge to a generalized, the so-called dissipative weak, solution of the original problem. If a strong solution exists, the dissipative weak solution emanating from the same initial data coincides with the strong solution. In this case, we apply a novel tool of the relative energy and derive the error estimates between the numerical solution and the strong solution. Extensive numerical experiments that confirm theoretical results are presented.

Analysis and convergence of finite volume method using discontinuous bilinear functions

AbstractWe develop finite volume method using discontinuous bilinear functions on rectangular mesh. This method is analyzed for the Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh‐dependent norm. First order L2‐error estimates are derived for the approximations of both velocity and pressure. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007

다중격자 유한체적법에 의한 복사열전달 해석

The convergence of finite volume method (FVM) or discrete ordinatc method (DOM) is known to degrade for optical thickness greater than unity and large scattering albedo. The present article presents a convergence acceleration procedure for the FVM based on a full approximation storage (FAS) multigrid method. Among a variety of multigrid cycles, the V-cycle is used and the full multigrid algorithm (FMG) is applied to an analysis of radiation in irregular two-dimensional geometry. Solution convergence is discussed for the several cases of various optical thickness and scattering albedo. At small scattering albedo and optical thickness, there is no advantage to using the multigrid method for calculation CPU time. For large scattering albedo greater than 0.5 and optical thickness greater than unity, however, the multigrid method improves the convergence and the solution is rapidly obtained.<br/>