Efficient, Unconditionally Stable, and Optimally Accurate FE Algorithms for Approximate Deconvolution Models

نویسندگان

  • Keith J. Galvin
  • Leo G. Rebholz
  • Catalin Trenchea
چکیده

This paper addresses an open question of how to devise numerical schemes for approximate deconvolution fluid flow models that are efficient, unconditionally stable, and optimally accurate. We propose, analyze and test a scheme for these models that has each of these properties for the case of homogeneous Dirichlet velocity boundary conditions. There are several important components to the derivation, both at the continuous and discrete levels, which allow for these properties to hold. The proofs of unconditional stability and optimal convergence are carried out through the use of a special choice of test function and some technical estimates. Numerical tests are provided that confirm the effectiveness of the scheme.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Improving Numerical Accuracy in a Regularized Barotropic Vorticity Model of Geophysical Flow

We study the BV-α-Deconvolution model. It is a family of regularizations of the Barotropic Vorticity (BV) model that generalize the BV-α model and improve its accuracy. A both unconditionally stable and optimally convergent scheme for the BV-α-Deconvolution model is proposed and we show that it is O(α), where N is the deconvolution order, whereas the BV-α model is at most second order accurate....

متن کامل

On the split-step method for the solution of nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative

The aim of this paper is to extend the split-step idea for the solution of fractional partial differential equations. We consider the multidimensional nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative and propose an efficient numerical algorithm to obtain it's approximate solutions. To this end, we first discretize the Riesz fractional derivative then apply the Crank-...

متن کامل

Enabling numerical accuracy of the Navier-Stokes-α through deconvolution and enhanced stability

We propose and analyze a finite element method for approximating solutions to the NavierStokes-alpha model (NS-α) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly improves accuracy in simulations. Standard finite element schemes for NS-α suffer from two major sources of error if their solutions are considered approximations to true fluid flow: 1) the con...

متن کامل

Enabling numerical accuracy of Navier-Stokes-alpha through deconvolution and enhanced stability

We propose and analyze a finite element method for approximating solutions to the NavierStokes-alpha model (NS-α) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly improves accuracy in simulations. Standard finite element schemes for NS-α suffer from two major sources of error if their solutions are considered approximations to true fluid flow: 1) the con...

متن کامل

Software Cost Estimation by a New Hybrid Model of Particle Swarm Optimization and K-Nearest Neighbor Algorithms

A successful software should be finalized with determined and predetermined cost and time. Software is a production which its approximate cost is expert workforce and professionals. The most important and approximate software cost estimation (SCE) is related to the trained workforce. Creative nature of software projects and its abstract nature make extremely cost and time of projects difficult ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • SIAM J. Numerical Analysis

دوره 52  شماره 

صفحات  -

تاریخ انتشار 2014