International Journal for Numerical Methods in Fluids

Liu, T.G.; Khoo, B.C.; Yeo, K.S.

doi: 10.1002/(SICI)1097-0363(19991030)31:4<661::AID-FLD866>3.0.CO;2-Gpmid: N/A

Numerical simulations of explosion and implosion in air are carried out with a modified Harten's TVD scheme. The new scheme has a high resolution for contact discontinuities in addition to maintaining the good features of Harten's TVD scheme. In the numerical experiment of spherical explosion in air, the second shock wave (which does not exist in the one‐dimensional shock tube problem) and its subsequent implosion on the origin have been successfully captured. The positions of the main shock wave, the contact discontinuity and the second shock wave have shown satisfactory agreement with those predicted from previous analysis. The numerical results are also compared with those obtained experimentally. Finally, simulations of a cylindrical explosion and implosion in air are carried out. Results of the cylindrical implosion in air are compared with those of previous work, including the interaction of the reflected main shock wave with the contact discontinuity and the formation of a second shock wave. All these attest to the successful use of the modified Harten's TVD scheme for the simulations of shock waves arising from explosion and implosion. Copyright © 1999 John Wiley & Sons, Ltd.

Thevand, N.; Daniel, E.; Loraud, J.C.

doi: 10.1002/(SICI)1097-0363(19991030)31:4<681::AID-FLD893>3.0.CO;2-Kpmid: N/A

A high‐resolution numerical scheme based on the MUSCL–Hancock approach is developed to solve unsteady compressible two‐phase dilute viscous flow. Numerical considerations for the development of the scheme are provided. Several solvers for the Godunov fluxes are tested and the results lead to the choice of an exact Riemann solver adapted for both gaseous and dispersed phases. The accuracy of the scheme is proven step by step through specific test cases. These simulations are for one‐phase viscous flows over a flat plate in subsonic and supersonic regimes, unsteady flows in a low‐pressure shock tube, two‐phase dilute viscous flows over a flat plate and, finally, two‐phase unsteady viscous flows in a shock tube. The results are compared with well‐established analytical and numerical solutions and very good agreement is achieved. Copyright © 1999 John Wiley & Sons, Ltd.

Cornelius, C.; Volgmann, W.; Stoff, H.

doi: 10.1002/(SICI)1097-0363(19991030)31:4<703::AID-FLD895>3.0.CO;2-Dpmid: N/A

A numerical method for the efficient calculation of three‐dimensional incompressible turbulent flow in curvilinear co‐ordinates is presented. The mathematical model consists of the Reynolds averaged Navier–Stokes equations and the k–ε turbulence model. The numerical method is based on the SIMPLE pressure‐correction algorithm with finite volume discretization in curvilinear co‐ordinates. To accelerate the convergence of the solution method a full approximation scheme‐full multigrid (FAS‐FMG) method is utilized. The solution of the k–ε transport equations is embedded in the multigrid iteration. The improved convergence characteristic of the multigrid method is demonstrated by means of several calculations of three‐dimensional flow cases. Copyright © 1999 John Wiley & Sons, Ltd.

Chiang, T.P.; Sheu, Tony W.H.

doi: 10.1002/(SICI)1097-0363(19991030)31:4<721::AID-FLD897>3.0.CO;2-Bpmid: N/A

A numerical investigation of laminar flow over a backward‐facing step is presented within the transient context. The analysis is concerned with the step geometry and flow conditions reported by Armaly et al. Results show that there is generally good agreement between the three‐dimensional results and the experimental data for Re<400, and excellent agreement with the two‐dimensional results. Insight is also provided into the rich character of the end‐wall‐induced three‐dimensional vortices in the channel downstream of the step. To this end, the topological theory is adopted to draw the particle oil streaklines on the roof, floor, step plane and the end‐wall, from which lines of separation and reattachment are theoretically determined. Together with the Lagrangian particle track plot in the flow interior, light is shed on the formation of a secondary flow pattern, and thus the development of longitudinal vortices. The present transient analysis increases the understanding of the complex interaction of the end‐wall‐induced vortices and the mainstream flow. This helps to reveal the mechanism responsible for the increasing penetration of the three‐dimensional flow structure into a region near the mid‐plane of the channel, at which the flow is essentially two‐dimensional. Copyright © 1999 John Wiley & Sons, Ltd.

Chen, Yih‐Nan; Yang, Shih‐Chang; Yang, Jaw‐Yen

doi: 10.1002/(SICI)1097-0363(19991030)31:4<747::AID-FLD901>3.0.CO;2-Fpmid: N/A

A class of lower–upper/approximate factorization (LUAF) implicit weighted essentially non‐oscillatory (ENO; WENO) schemes for solving the two‐dimensional incompressible Navier–Stokes equations in a generalized co‐ordinate system is presented. The algorithm is based on the artificial compressibility formulation, and symmetric Gauss–Seidel relaxation is used for computing steady state solutions while symmetric successive overrelaxation is used for treating time‐dependent flows. WENO spatial operators are employed for inviscid fluxes and central differencing for viscous fluxes. Internal and external viscous flow test problems are presented to verify the numerical schemes. The use of a WENO spatial operator not only enhances the accuracy of solutions but also improves the convergence rate for the steady state computation as compared with using the ENO counterpart. It is found that the present solutions compare well with exact solutions, experimental data and other numerical results. Copyright © 1999 John Wiley & Sons, Ltd.

Hwang, Robert R.; Chow, Y.C.; Peng, Y.F.

doi: 10.1002/(SICI)1097-0363(19991030)31:4<767::AID-FLD902>3.0.CO;2-Apmid: N/A

This study accurately predicts the cases of turbulent flow around a surface‐mounted two‐dimensional rib with varying lengths. The numerical method employs a differencing scheme for integrating the elliptic Reynolds‐averaged Navier–Stokes equations and the continuity equation. A two‐equation k–ε turbulence model is employed to simulate the turbulent transport quantities and close the solving problem. The near‐wall regions of the separated sides of the rib are resolved by a near‐wall model of a two‐layer approach instead of the wall function approximation. Computations for flow over a surface‐mounted rectangular rib are conducted for the variations in the rib lengths. Results indicate that upstream of the obstacle, the length of the recirculating region remains unchanged with varying rib lengths; while the downstream length of the recirculating region is a strong function of rib length and changes nearly linearly for the varying lengths of B/H=0.1 to B/H=4.0. Reattachment on top of the rib, owing to its increasing length, affects the downstream boundary layer development. Copyright © 1999 John Wiley & Sons, Ltd.