Hidetoshi Nishida

Incompressible Flow Simulations Using Virtual Boundary Method with New Direct Forcing Terms Estimation

In this paper, a new external forcing terms estimation in the virtual boundary method is proposed. In the usual virtual boundary method with feedback and direct forcing terms estimations, the unphysical oscillations near the boundary appear in the pressure field.In order to remove these unphysical oscillations, the new direct forcing terms are added not only near the boundary but also inside the boundary. In the incompressible flows past a circular cylinder and a sphere, the pressure oscillations near the boundary can be removed and the flow characteristics on the boundary are in very good agreement with the reference results.

A Variable Order Method of Lines: Accuracy, Conservation and Applications

The variable order method of lines is presented for the DNS of incompressible flows. The present method is constructed by the spatial discretization, i.e., the variable order proper convective scheme and modified differential quadrature method, and time integration. The accuracy and conservation property are validated in the 2D Taylor-Green solutions and 3D homogeneous isotropic turbulence. As applications, the flows around a circular cylinder and a sphere are simulated by using Cartesian grid approach with virtual boundary method. Consequently, the present method is very promising for the DNS of the incompressible flows

Numerical Analysis of Particle Behavior Penetrating into Liquid by Level Set Method

A numerical analysis technique using the level set method has been developed to calculate the critical velocity of a particle penetrating into liquid. The contact angle, a dominant factor in this phenomenon, is given by imaginary gas-liquid interfaces inside a solid wall. A Cartesian grid method with immersed boundary is also applied in order to accurately represent a boundary of a moving particle. The current results agree with other calculated and experimental results in contact-angle problems. Finally, calculations of a particle impinging on a liquid surface have been carried out. Current results of the critical velocity agree with experimental and theoretical results.

Cartesian Grid Approach with Virtual Boundary Method and Its Applications

The DNSs of the incompressible flows are performed by using the Cartesian grid approach with virtual boundary method. In the virtual boundary method, the body surface is expressed by a set of plural points, and the velocity components on virtual boundary are feedbacked to the momentum equations as the additional forcing terms. In order to validate the present method, the DNSs of flow around a circular cylinder are considered. The flow characteristics are in very good agreement with the other DNS results. Next, the present method is applied to the DNSs of flows around a sphere and two spheres. In the flow around a sphere, the flow characteristics are in excellent agreement with other numerical and experimental results, and it is clearly observed that the hairpin vortex ring is released and the flow transits from laminar to turbulence in Re = 1000. It is shown in the flow around two spheres that the released vortex rings interfere each other. Consequently, the present method is very promising for the DNSs of the incompressible complicated flow.

Numerical solution of unsteady incompressible Navier-Stokes equations using high-order method of lines

Abstract A high-order method of lines is devised for solving the unsteady incompressible Navier-Stokes equations in the vorticity-stream function formulation. The vorticity transport equation is solved by the eight- or tenth-order method of lines and the Poisson equation for the stream function is solved by a high-order multigrid method. The numerical results of the two-dimensional (2D) homogeneous isotropic turbulence and the turbulent mixing layer are presented. In the homogeneous isotropic turbulence with tenth order of spatial accuracy, the power law of the inertial energy spectrum at the climax stage coincides with the predictions by Batchelor, Leith and Kraichnan. In the turbulent mixing layer with eight order of spatial accuracy, the vortex pairing are reproduced and the coherent structure of the Reynolds stress at the pairing is noticed.

Higher-order method of lines for the numerical simulation of turbulence

A new method is devised for the numerical simulation of turbulences. The spatial derivatives of the time-dependent incompressible Navier-Stokes equations are discretized by using the modified differential quadrature (MDQ) method. The resulting system of ordinary differential equations in time are then integrated by a class of fourth order explicit Runge-Kutta schemes. The simulations of two and three-dimensional homogeneous isotropic turbulence suggest that the present method is more efficient and versatile than the pseudospectral method.

Parallel Efficiency of a Variable Order Method of Lines

The parallel efficiency of a variable order method of lines on parallel platforms is investigated. The variable order method of lines shows the 91% parallel efficiency on Pilot-3 system and gives 46.3 times speed up on SSCMPP system. DNS of 3-D homogeneous isotropic turbulence is carried out. The parallel DNSs at 2563 grid resolution are carried out successfully on the parallel platform with 256 PEs. In comparison with the spectral solutions, the present higher order method is as accurate as the spectral method at comparable resolution.

Higher Order Parallel DNS of Incompressible Turbulence Using Compressible Navier-Stokes Equations

Publisher Summary This chapter discusses development of compressible Navier–Stokes equations into the direct numerical simulations (DNSs) of incompressible turbulence. The higher order parallel DNS of incompressible turbulence based on the compressible Navier–Stokes equations is carried out. The governing equations are solved by the higher order method of lines with shifted flux technique. By using the shifted flux technique, it is possible to obtain very smooth solution without the unphysical oscillations. The present higher order solutions are compared with the higher order incompressible ones obtained by the variable order method of lines. In the implementation on a parallel platform, the approach shows almost theoretical scalability on the ITBL machine with shared memory system at Japan Atomic Energy Research Institute (JAERI). The compressible approach can shorten computational time in comparison with the incompressible approach on a scalar machine, too. It is concluded that the higher order compressible approach is very promising for the simulation of incompressible flows.

Large-scale direct simulation of two-dimensional homogeneous isotropic turbulence using a higher-order method of lines.

A new higher order method is devised for the numerical simulation of two-dimensional homogeneous isotropic turbulence. The spatial derivatives of the Navier-Stokes equations are discretized by means of the modified differential quadrature (MDQ) method. The resulting system of ordinary differential equations in time is integrated by the fourth-order Runge-Kutta-Gill (RKG) schemes. The elliptic (Poisson) equation in solved by a new variable-order multigrid method. The direct simulations are presented at resolutions up to 1024×1024. The results suggest that the present higher order method is more efficient, and that the history of the vorticity field consists of three stages, i. e., development, peak, and decay. The corresponding power laws of inertial energy spectrum are k-4, k-3, and k-4, respectively.

Comparison of Handling Pressure in Poisson Solver for Immersed Boundary Method Considering Pressure Condition

Abstract In the Cartesian grid approach, the immersed boundary method (IBM) is well used to handle the boundary of an object with complicated shape on the Cartesian grid. However, the conventional IBM generates the unphysical pressure oscillations near the boundary because of the pressure jump between inside and outside of the boundary. The IBM considering pressure condition was proposed in order to remove the pressure oscillations by solving the governing equations considering the pressure condition on the boundary. In this method, there are two ways of the handling the pressure on the boundary in the Poisson solver. In this paper, the effect of removing the pressure oscillations by the IBM considering the pressure condition is investigated. And, the influence by the difference in the handling of the pressure on the boundary in the Poisson solver is investigated. In the numerical simulations of incompressible flow around a 2D circular cylinder, the present IBM indicates a greate effect of removing the pressure oscillations. And, it does not occur difference of the result by the difference of the handling the pressure on the boundary in the Poisson solver. Therefore, it is possible to select a method with less computational amount in the Poisson solver without degrading the quality of the result. It is concluded that the present IBM is very promising as improved method in order to remove the pressure oscillations in the conventional IBM.