Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAnalysis and computation of a pressure-robust method for the rotation form of the stationary incompressible Navier-Stokes equations by using high-order finite elements
230
0
0.0
(
0
)
Added by
Di Yang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this work, we develop a high-order pressure-robust method for the rotation form of the stationary incompressible Navier-Stokes equations. The original idea is to change the velocity test functions in the discretization of trilinear and right hand side terms by using an H(div)-conforming velocity reconstruction operator. In order to match the rotation form and error analysis, a novel skew-symmetric discrete trilinear form containing the reconstruction operator is proposed, in which not only the velocity test function is changed. The corresponding well-posed discrete weak formulation stems straight from the classical inf-sup stable mixed conforming high-order finite elements, and it is proven to achieve the pressure-independent velocity errors. Optimal convergence rates of H1, L2-error for the velocity and L2-error for the Bernoulli pressure are completely established. Adequate numerical experiments are presented to demonstrate the theoretical results and the remarkable performance of the proposed method.
rate research
Read More
We propose an efficient, accurate and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is demonstrated in a number of classical benchmarks, which highlight its superior efficiency with respect to other widely used implicit approaches. The parallel implementation of the proposed method in the framework of the deal.II software package allows for accurate and efficient adaptive simulations in complex geometries, which makes the proposed solver attractive for large scale industrial applications.
In two dimensions, we propose and analyze an a posteriori error estimator for finite element approximations of the stationary Navier Stokes equations with singular sources on Lipschitz, but not necessarily convex, polygonal domains. Under a smallness assumption on the continuous and discrete solutions, we prove that the devised error estimator is reliable and locally efficient. We illustrate the theory with numerical examples.
We propose and study numerically the implicit approximation in time of the Navier-Stokes equations by a Galerkin-collocation method in time combined with inf-sup stable finite element methods in space. The conceptual basis of the Galerkin-collocation approach is the establishment of a direct connection between the Galerkin method and the classical collocation methods, with the perspective of achieving the accuracy of the former with reduced computational costs in terms of less complex algebraic systems of the latter. Regularity of higher order in time of the discrete solution is ensured further. As an additional ingredient, we employ Nitsches method to impose all boundary conditions in weak form with the perspective that evolving domains become feasible in the future. We carefully compare the performance poroperties of the Galerkin-collocation approach with a standard continuous Galerkin-Petrov method using piecewise linear polynomials in time, that is algebraically equivalent to the popular Crank-Nicholson scheme. The condition number of the arising linear systems after Newton linearization as well as the reliable approximation of the drag and lift coefficient for laminar flow around a cylinder (DFG flow benchmark with $Re=100$) are investigated. The superiority of the Galerkin-collocation approach over the linear in time, continuous Galerkin-Petrov method is demonstrated therein.
We present a residual-based a posteriori error estimator for the hybrid high-order (HHO) method for the Stokes model problem. Both the proposed HHO method and error estimator are valid in two and three dimensions and support arbitrary approximation orders on fairly general meshes. The upper bound and lower bound of the error estimator are proved, in which proof, the key ingredient is a novel stabilizer employed in the discrete scheme. By using the given estimator, adaptive algorithm of HHO method is designed to solve model problem. Finally, the expected theoretical results are numerically demonstrated on a variety of meshes for model problem.
This paper will suggest a new finite element method to find a $P^4$-velocity and a $P^3$-pressure solving incompressible Stokes equations at low cost. The method solves first the decoupled equation for a $P^4$-velocity. Then, using the calculated velocity, a locally calculable $P^3$-pressure will be defined component-wisely. The resulting $P^3$-pressure is analyzed to have the optimal order of convergence. Since the pressure is calculated by local computation only, the chief time cost of the new method is on solving the decoupled equation for the $P^4$-velocity. Besides, the method overcomes the problem of singular vertices or corners.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
