scholarly journals SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization

Water ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 245
Author(s):  
Antonio Eirís ◽  
Luis Ramírez ◽  
Javier Fernández-Fidalgo ◽  
Iván Couceiro ◽  
Xesús Nogueira
Keyword(s):  
Viscous Flow ◽  
Optimal Order ◽  
A Posteriori ◽  
Riemann Problems ◽  
Driven Cavity ◽  
Flux Limiter ◽  
Ideal Gases ◽  
Weakly Compressible ◽  
Order Variable ◽  
Convective Fluxes

A highly accurate SPH method with a new stabilization paradigm has been introduced by the authors in a recent paper aimed to solve Euler equations for ideal gases. We present here the extension of the method to viscous incompressible flow. Incompressibility is tackled assuming a weakly compressible approach. The method adopts the SPH-ALE framework and improves accuracy by taking high-order variable reconstruction of the Riemann states at the midpoints between interacting particles. The moving least squares technique is used to estimate the derivatives required for the Taylor approximations for convective fluxes, and also provides the derivatives needed to discretize the viscous flux terms. Stability is preserved by implementing the a posteriori Multi-dimensional Optimal Order Detection (MOOD) method procedure thus avoiding the utilization of any slope/flux limiter or artificial viscosity. The capabilities of the method are illustrated by solving one- and two-dimensional Riemann problems and benchmark cases. The proposed methodology shows improvements in accuracy in the Riemann problems and does not require any parameter calibration. In addition, the method is extended to the solution of viscous flow and results are validated with the analytical Taylor–Green, Couette and Poiseuille flows, and lid-driven cavity test cases.

A posteriori error estimates for viscous flow problems with rotation

2007 ◽  
Vol 142 (1) ◽  
pp. 1749-1762 ◽  
Author(s):  
E. Gorshkova ◽  
A. Mahalov ◽  
P. Neittaanmäki ◽  
S. Repin
Keyword(s):  
Viscous Flow ◽  
Error Estimates ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Flow Problems

scholarly journals Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations

2004 ◽  
Vol 2004 (37) ◽  
pp. 1973-1996 ◽  
Author(s):  
Santhosh George ◽  
M. Thamban Nair
Keyword(s):  
Wide Class ◽  
Noise Level ◽  
A Priori ◽  
Approximate Solutions ◽  
Optimal Order ◽  
Discrepancy Principle ◽  
A Posteriori ◽  
Operator Equations ◽  
Finite Dimensional ◽  
Ill Posed

Simplified regularization using finite-dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill-posed operator equations. The derived error estimates using an a priori and a posteriori choice of parameters in relation to the noise level are shown to be of optimal order with respect to certain natural assumptions on the ill posedness of the equation. The results are shown to be applicable to a wide class of spline approximations in the setting of Sobolev scales.

scholarly journals The use of dual reciprocity method for 2D laminar viscous flow

2020 ◽  
Vol 310 ◽  
pp. 00044
Author(s):  
Juraj Mužík
Keyword(s):  
Viscous Flow ◽  
Flow Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Singular Boundary ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Boundary Method ◽  
2D Flow ◽  
Singular Boundary Method

The paper presents the use of the dual reciprocity multidomain singular boundary method (SBMDR) for the solution of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using a singular boundary method with the 2D Stokes fundamental solution - Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the nonhomogeneous and nonlinear terms of Navier-Stokes equations. The presented SBMDR approach to the solution of the 2D flow problem is demonstrated on a standard benchmark problem - lid-driven cavity.

scholarly journals COMPLEXITY ESTIMATES FOR SEVERELY ILL-POSED PROBLEMS UNDER A POSTERIORI SELECTION OF REGULARIZATION PARAMETER

2017 ◽  
Vol 22 (3) ◽  
pp. 283-299
Author(s):  
Sergii G. Solodky ◽  
Ganna L. Myleiko ◽  
Evgeniya V. Semenova
Keyword(s):  
Integral Equations ◽  
Regularization Parameter ◽  
Efficient Algorithms ◽  
Optimal Order ◽  
A Posteriori ◽  
Order Of Accuracy ◽  
Tikhonov Method ◽  
Discrete Information ◽  
Ill Posed ◽  
Selection Of

In the article the authors developed two efficient algorithms for solving severely ill-posed problems such as Fredholm’s integral equations. The standard Tikhonov method is applied as a regularization. To select a regularization parameter we employ two different a posteriori rules, namely, discrepancy and balancing principles. It is established that proposed strategies not only achieved optimal order of accuracy on the class of problems under consideration, but also they are economical in the sense of used discrete information.

A Modified Smoothed Particle Hydrodynamics Scheme to Model the Stationary and Moving Boundary Problems for Newtonian Fluid Flows

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Mohammad Sefid ◽  
Rouhollah Fatehi ◽  
Rahim Shamsoddini
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Moving Boundary ◽  
Fluid Flows ◽  
Boundary Problems ◽  
Driven Cavity ◽  
First Case ◽  
Weakly Compressible ◽  
Present Solution ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

A robust modified weakly compressible smoothed particle hydrodynamics (WCSPH) method based on a predictive corrective scheme is introduced to model the fluid flows engaged with stationary and moving boundary. In this paper, this model is explained and practically verified in three distinct laminar incompressible flow cases; the first case involves the lid driven cavity flow for two Reynolds numbers 400 and 1000. The second case is a flow generated by a moving block in the initially stationary fluid. The third case is flow around the stationary and transversely oscillating circular cylinder confined in a channel. These results in comparison with the standard benchmarks also confirm the good accuracy of the present solution algorithm.

scholarly journals A posteriori analysis for space-time, discontinuous in time Galerkin approximations for parabolic equations in a variable domain

2019 ◽  
Vol 53 (2) ◽  
pp. 523-549 ◽  
Author(s):  
Dimitra Antonopoulou ◽  
Michael Plexousakis
Keyword(s):  
Error Bounds ◽  
A Priori Estimates ◽  
American Mathematical Society ◽  
Parabolic Type ◽  
Space Time ◽  
Parabolic Problems ◽  
Optimal Order ◽  
Cylindrical Domain ◽  
A Posteriori ◽  
Time Space

This paper presents an a posteriori error analysis for the discontinuous in time space–time scheme proposed by Jamet for the heat equation in multi-dimensional, non-cylindrical domains Jamet (SIAM J. Numer. Anal. 15 (1978) 913–928). Using a Clément-type interpolant, we prove abstract a posteriori error bounds for the numerical error. Furthermore, in the case of two-dimensional spatial domains we transform the problem into an equivalent one, of parabolic type, with space-time dependent coefficients but posed on a cylindrical domain. We formulate a discontinuous in time space–time scheme and prove a posteriori error bounds of optimal order. The a priori estimates of Evans (American Mathematical Society (1998)) for general parabolic initial and boundary value problems are used in the derivation of the upper bound. Our lower bound coincides with that of Picasso (Comput. Meth. Appl. Mech. Eng. 167 (1998) 223–237), proposed for adaptive, Runge-Kutta finite element methods for linear parabolic problems. Our theoretical results are verified by numerical experiments.

Numerical Simulation of Viscous Flow in a 3D Lid-Driven Cavity Using Lattice Boltzmann Method

2013 ◽  
Vol 444-445 ◽  
pp. 395-399
Author(s):  
Di Bo Dong ◽  
Sheng Jun Shi ◽  
Zhen Xiu Hou ◽  
Wei Shan Chen
Keyword(s):  
Reynolds Number ◽  
Viscous Flow ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Primary Vortex ◽  
Driven Cavity ◽  
Single Relaxation Time ◽  
Moderate Reynolds Number ◽  
Boltzmann Method

A lattice Boltzmann method (LBM) with single-relaxation time and on-site boundary condition is used for the simulation of viscous flow in a three-dimensional (3D) lid-driven cavity. Firstly, this algorithm is validated by compared with the benchmark experiments for a standard cavity, and then the results of a cubic cavity with different inflow angles are presented. Steady results presented are for the inflow angle of and, and the Reynolds number is selected as 500. It is found that for viscous flow under moderate Reynolds number, there exists a primary vortex near the center and a secondly vortex at the lower right corner on each slice when, namely in a standard 3D lid-driven cavity, which cant be found when. So it can be thought that the flow pattern in a 3D lid-driven cavity depends not only on the Reynolds number but also the inflow angle.

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