Solution Of Fluid Dynamic Equations Research Articles

Special Issue Editorial: Small Scales and Singularity Formation in Fluid Dynamics

We review recent advances in understanding singularity and small scales formation in solutions of fluid dynamics equations. The focus is on the Euler and surface quasi-geostrophic (SQG) equations and associated models.

Cusps and cuspidal edges at fluid interfaces: Existence and application.

One of the intriguing questions in fluid dynamics is on the interrelation between dynamic singularities in the solutions of fluid dynamic equations - unboundedness of the velocity field in an appropriate norm - and the geometric ones - divergence of curvature at fluid interfaces. The present work focuses on two generic interfacial singularities - genuine cusps and cuspidal edges - found here in both two and three dimensions thus establishing a relation between real fluid interfaces and geometric singularity theory. The key finding is the necessary condition for the existence of geometric singularities, which is a variation of surface tension. It is also established here that the dynamic and geometric singularities entail each other only in the case of three-dimensional cusps. Explicit asymptotic solutions for the flow field and interface shape near steady-state singularities at fluid interfaces are developed as well. The practical motivation for the present study comes from the fundamental role interfacial singularities play in sustaining self-driven conversion of chemical into mechanical energy.

Computation of discontinuous solutions of fluid dynamics equations with entropy nondecrease guarantee

A new formulation of the Godunov scheme with linear Riemann problems is proposed that guarantees a nondecrease in entropy. The new version of the method is described for the simplest example of one-dimensional gas dynamics in Lagrangian coordinates.

Optimization of LU-SGS Code for the Acceleration on the Modern Microprocessors

An approach for composing a performance optimized computational code is suggested for the latest microprocessors. The concept of the code optimization, termed localization, is maximizing the utilization of the second level cache that is common to all the latest computer systems, and minimizing the access to system main memory. In this study, the localized optimization of the LU-SGS (Lower-Upper Symmetric Gauss-Seidel) code for the solution of fluid dynamic equations was carried out in three different levels and tested for several different microprocessor architectures widely used these days. The test results of localized optimization showed a remarkable performance gain of more than two times faster solution than the baseline algorithm for producing exactly the same solution on the same computer system.

Validation of CFD‐CSD coupling interface methodology using commercial codes

AbstractCoupling interface between computational fluid dynamics (CFD) and computational structural dynamics (CSD) is required to provide exchange of information for the simulation of fluid–structure interaction (FSI) phenomena. Accuracy and consistency of information exchanged through coupling interface between the independent CFD and CSD solvers plays a central role in the simulation and prediction of FSI phenomenon, like flutter. In this paper validation of an implemented coupling interface methodology is presented for subsonic, transonic and near supersonic mach regime. The test case chosen for this purpose is the flutter of AGARD445.6 standard I‐wing weakened model configuration for subsonic to near transonic flow regime. Gambit® and Fluent® are used for CFD grid generation and solution of fluid dynamic equations, respectively. CSD modeling and simulation are provided by numerical time integration of modal dynamic equations derived through the finite element modeling in ANSYS® environment. Copyright © 2009 John Wiley & Sons, Ltd.

On critical reynolds numbers in plane channels with a sudden expansion at the entry

A method for the numerical solution of fluid dynamics equations is proposed. The evolution of the structure of the laminar flow with increasing Reynolds number and its behavior at the critical Reynolds number Recris analyzed. Various flow modes at Re = Recr are discussed.

Ovsyannikov plane vortex: The equations of the submodel

In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture of motion is relatively simple: trajectory of one fluid particle from plane x=const completely determines motion of the whole plane. Basing on the symmetry analysis of differential equations we propose generalization of this solution allowing movements in different directions of fluid particles belonging to plane x=const. At that, all functions but an angle determining the direction of particle's motion depend on t and x only, whereas the angle depends on all coordinates. In this solution the whole picture of motion superposes from identical trajectories placed under different angles in 3D space. Orientations of the trajectories are restricted by a finite relation possessing functional arbitrariness. The solution describes three-dimensional nonlinear processes and singularities in infinitely conducting plasma, gas or incompressible liquid.

Computing nearly singular solutions using pseudo-spectral methods

In this paper, we investigate the performance of pseudo-spectral methods in computing nearly singular solutions of fluid dynamics equations. We consider two different ways of removing the aliasing errors in a pseudo-spectral method. The first one is the traditional 2/3 dealiasing rule. The second one is a high (36th) order Fourier smoothing which keeps a significant portion of the Fourier modes beyond the 2/3 cut-off point in the Fourier spectrum for the 2/3 dealiasing method. Both the 1D Burgers equation and the 3D incompressible Euler equations are considered. We demonstrate that the pseudo-spectral method with the high order Fourier smoothing gives a much better performance than the pseudo-spectral method with the 2/3 dealiasing rule. Moreover, we show that the high order Fourier smoothing method captures about 12–15% more effective Fourier modes in each dimension than the 2/3 dealiasing method. For the 3D Euler equations, the gain in the effective Fourier codes for the high order Fourier smoothing method can be as large as 20% over the 2/3 dealiasing method. Another interesting observation is that the error produced by the high order Fourier smoothing method is highly localized near the region where the solution is most singular, while the 2/3 dealiasing method tends to produce oscillations in the entire domain. The high order Fourier smoothing method is also found be very stable dynamically. No high frequency instability has been observed. In the case of the 3D Euler equations, the energy is conserved up to at least six digits of accuracy throughout the computations.

Modern Trends in CFD Simulations: Application to GTL Technology

Multiphase flow processes are frequently observed in several important reactor technologies. These technologies are found in diverse applications such as in manufacture of petroleum-based fuels and products, conversion of synthesis gas into liquid hydrocarbons (Gas-to-liquid technology), production of commodity chemicals, pharmaceuticals, herbicides, pesticides, polymers etc. Due to the inherent complexity of these processes, the knowledge of fluid dynamic and transport parameters is necessary for development of appropriate reactor models and scale-up rules. It is, therefore, of paramount importance to develop understanding and predictive tools to simulate multiphase flow processes for better and economically viable reactor technologies. In the past, knowledge of hydrodynamics and transport characteristics of multiphase reactors has been interpreted in the form of empirical correlations, which have numerous restrictions in terms of their validity for different operating conditions. Computational fluid dynamics (CFD) simulation, on the other hand, deals with the solution of fluid dynamic equations on digital computers, requiring relatively few restrictive assumptions and thus giving a complete description of the hydrodynamics of these reactors. This detailed predicted flow field gives an accurate insight to the fluid behaviour and can sometimes give information, which cannot be obtained from experiments. These days, due to cheaper computational resources, CFD simulations are becoming economically reliable for modeling of multiphase processes including GTL (Gas-to-liquid) processes. In this paper, a comprehensive review of different multiphase flow simulation approaches has been presented. The recent progress made in hydrodynamic modeling of multiphase reactors, their capabilities and limitations (with special focus on GTL processes) are discussed in detail. Finally, case studies with different simulation approaches (Eulerian-Eulerian and VOF (Volume of fluid) simulations of bubble column reactors operating in different flow regimes) are discussed to demonstrate the power of this emerging research tool.

최신 마이크로프로세서에서 2차 캐쉬 적중률 증가를 고려한 LU-SGS 코드의 가속

An approach for composing a performance optimized computational code is suggested for latest microprocessors. The concept of the code optimization, called here as localization, is maximizing the utilization of the second level cache that is common to all the latest computer system, and minimizing the access to system main memory. In this study, the localized optimization of LU-SGS (Lower-Upper Symmetric Gauss-Seidel) code for the solution of fluid dynamic equations was carried out in three different levels and tested for several different microprocessor architectures most widely used in these days. The test results of localized optimization showed a remarkable performance gain up to 7.35 times faster solution, depending on the system, than the baseline algorithm for producing exactly the same solution on the same computer system.

Effect of artificial viscosity on three-dimensional flow solutions

Artificial viscosity is added either implicity or explicitly in practically every numerical scheme for suppressing spurious oscillations in the solution of fluid-dynamics equations. In the present central-difference scheme, artificial viscosity is added explicitly for suppressing high-frequency oscillations and achieving good convergence properties. The amount of artificial viscosity added is controlled through the use of preselected coefficients. In the standard scheme, scalar coefficients based on the spectral radii of the Jacobian of the convective fluxes are used. However, this can add too much viscosity to the slower waves. Hence, the use of matrix-valued coefficients, which give appropriate viscosity for each wave component, is suggested. With the matrix-valued coefficients, the central-difference scheme produces more accurate solutions on a given grid, particularly in the vicinity of shocks and boundary layers, while still maintaining good convergence properties.

Large-scale method of lines solution of fluid dynamic equations on Japanese supercomputers

A method of lines approach is proposed for the numerical simulation of the fluid dynamic equations on supercomputers. The method consists of the finite difference approximation to the spatial derivatives and subsequent time integrations by an appropriate numerical scheme. Numerical results are presented to demonstrate the utility of the present approach.

Efficient High-Order Method for the Solution of Fluid Dynamics Equations

An asymmetric weighted residual method for the solution of fluid dynamics equations is described that leads to local operators with a finite difference structure independent of the degree of approximating polynomials. It combines high accuracy on a coarse computational mesh and short computing time per space point and thus brings about sizable reductions of running time, relative to conventional methods.