Supercomputing of Supersonic Flows Using Upwind Relaxation and MacCormack Schemes

1988 ◽  
Vol 110 (1) ◽  
pp. 62-68 ◽  
Author(s):  
Oktay Baysal
Keyword(s):  
Stokes Equations ◽  
Supersonic Flows ◽  
Navier Stokes ◽  
Computational Algorithms ◽  
Navier Stokes Equations ◽  
Relaxation Scheme ◽  
Finite Volume Discretization ◽  
Finite Difference Discretization ◽  
The Mathematical Model ◽  
Difference Discretization

The impetus of this paper is the comparative applications of two numerical schemes for supersonic flows using computational algorithms tailored for a supercomputer. The mathematical model is the conservation form of Navier-Stokes equations with the effect of turbulence being modeled algebraically. The first scheme is an implicit, unfactored, upwind-biased, line-Gauss-Seidel relaxation scheme based on finite-volume discretization. The second scheme is the explicit-implicit MacCormack scheme based on finite-difference discretization. The best overall efficiences are obtained using the upwind relaxation scheme. The integrity of the solutions obtained for the example cases is shown by comparisons with experimental and other computational results.

Mathematical study of a single leukocyte in microchannel flow

2018 ◽  
Vol 13 (5) ◽  
pp. 43 ◽  
Author(s):  
S. Boujena ◽  
O. Kafi ◽  
A. Sequeira
Keyword(s):  
Mathematical Model ◽  
Numerical Approximation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Microchannel Flow ◽  
Navier Stokes Equations ◽  
Coupled Problem ◽  
Inflammatory Drugs ◽  
The Mathematical Model ◽  
Rate Type

The recruitment of leukocytes and subsequent rolling, activation, adhesion and transmigration are essential stages of an inflammatory response. Chronic inflammation may entail atherosclerosis, one of the most devastating cardiovascular diseases. Understanding this mechanism is of crucial importance in immunology and in the development of anti-inflammatory drugs. Micropipette aspiration experiments show that leukocytes behave as viscoelastic drops during suction. The flow of non-Newtonian viscoelastic fluids can be described by differential, integral and rate-type constitutive equations. In this study, the rate-type Oldroyd-B model is used to capture the viscoelasticity of the leukocyte which is considered as a drop. Our main goal is to analyze a mathematical model describing the deformation and flow of an individual leukocyte in a microchannel flow. In this model we consider a coupled problem between a simplified Oldroyd-B system and a transport equation which describes the density considered as non constant in the Navier–Stokes equations. First we present the mathematical model and we prove the existence of solution, then we describe its numerical approximation using the level set method. Through the numerical simulations we analyze the hemodynamic effects of three inlet velocity values. We note that the hydrodynamic forces pushing the cell become higher with increasing inlet velocities.

Analysis of the Roll Decay Motion for a Patrol Boat by URANS Simulations

2009 ◽  
Author(s):  
Riccardo Broglia ◽  
Roberto Muscari ◽  
Andrea Di Mascio
Keyword(s):  
Single Phase ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Roll Motion ◽  
Navier Stokes Equations ◽  
Roll Moment ◽  
Finite Volume Discretization ◽  
Grid Convergence ◽  
Unsteady Rans

The simulations of the flow around a vessel of the Italian Navy in free roll decay have been carried out by the numerical solution of the Reynolds Averaged Navier-Stokes equations. The focus is on the analysis of the roll motion coefficients (damping and period of oscillations) at different Froude and Reynolds numbers. To this aim, numerical simulations were carried out at three different speeds, with corresponding Froude numbers equal to 0.160, 0.227 and 0.337, and Reynolds numbers ranging from 4.073 106 to 1.300 107 at model scale. Computations were carried out by means of an in-house unsteady RANS solver; the scheme is based on a finite volume discretization, and it is globally second order accurate. The free surface is handled by means of a suitable single phase level set algorithm; moreover, Chimera overlapping grid capabilities have been implemented in the code, which has been also efficiently parallelized. An analysis of the roll motion, longitudinal and lateral forces and roll moment is carried out for the different speeds considered. A preliminarily grid convergence analysis is also performed.

Influences of lateral jet location and its number on the drag reduction of a blunted body in supersonic flows

2020 ◽  
Vol 124 (1277) ◽  
pp. 1055-1069 ◽  
Author(s):  
M. Dong ◽  
J. Liao ◽  
Z. Du ◽  
W. Huang
Keyword(s):  
Drag Reduction ◽  
Drag Force ◽  
Blunt Body ◽  
Stokes Equations ◽  
Supersonic Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduction Strategies ◽  
Promising Application ◽  
Force Reduction

ABSTRACTThe analysis of the aerodynamic environment of the re-entry vehicle attaches great importance to the design of the novel drag reduction strategies, and the combinational spike and jet concept has shown promising application for the drag reduction in supersonic flows. In this paper, the drag force reduction mechanism induced by the combinational spike and lateral jet concept with the freestream Mach number being 5.9332 has been investigated numerically by means of the two-dimensional axisymmetric Navier-Stokes equations coupled with the shear stress transport (SST) k-ω turbulence model, and the effects of the lateral jet location and its number on the drag reduction of the blunt body have been evaluated. The obtained results show that the drag force of the blunt body can be reduced more profoundly when employing the dual lateral jets, and its maximum percentage is 38.81%, with the locations of the first and second lateral jets arranged suitably. The interaction between the leading shock wave and the first lateral jet has a great impact on the drag force reduction. The drag force reduction is more evident when the interaction is stronger. Due to the inclusion of the lateral jet, the pressure intensity at the reattachment point of the blunt body decreases sharply, as well as the temperature near the walls of the spike and the blunt body, and this implies that the multi-lateral jet is beneficial for the drag reduction.

scholarly journals Dynamic Response of Base-Isolated Concrete Rectangular Liquid-Storage Structure Under Large Amplitude Sloshing

2017 ◽  
Vol 63 (1) ◽  
pp. 33-45 ◽  
Author(s):  
Xuansheng Cheng ◽  
De Li ◽  
Peijiang Li ◽  
Xiaoyan Zhang ◽  
Guoliang Li
Keyword(s):  
Wave Height ◽  
Large Amplitude ◽  
Stokes Equations ◽  
Seismic Intensity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Storage Structure ◽  
Liquid Storage ◽  
Rectangular Liquid Storage Structure ◽  
The Mathematical Model

AbstractConsidering concrete nonlinearity, the wave height limit between small and large amplitude sloshing is defined based on the Bernoulli equation. Based on Navier-Stokes equations, the mathematical model of large amplitude sloshing is established for a Concrete Rectangle Liquid-Storage Structure (CRLSS). The results show that the seismic response of a CRLSS increases with the increase of seismic intensity. Under different seismic fortification intensities, the change in trend of wave height, wallboard displacement, and stress are the same, but the amplitudes arc not. The areas of stress concentration appear mainly at the connections between the wallboards, and the connections between the wallboard and the bottom.

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