B.C. Khoo

Ghost fluid method for strong shock impacting on material interface

It is found that the original ghost fluid method (GFM) as put forth by Fedkiw et al. [J. Comp. Phys. 152 (1999) 457] does not work consistently and efficiently using isentropic fix when applied to a strong shock impacting on a material interface. In this work, the causes for such inapplicability of the original GFM are analysed and a modified GFM is proposed and developed for greater robustness and consistency. Numerical tests also show that the modified GFM has the property of reduced conservation error and is less problem-related.

The simulation of compressible multi-medium flow: II. Applications to 2D underwater shock refraction

Abstract In this work, the methodology developed in Part I [Comp. Fluids (2000), submitted for publication] is applied to study underwater shock refracting at a gas–water interface. The reflected wave is always a shock (rarefaction) wave if a shock (rarefaction) wave enters from a gas medium into water, while the reflected wave is always a rarefaction (compression) wave if the incident shock (rarefaction) wave enters from water into a gas medium. In the first study of a vertical planar underwater shock interacting with a cylindrical gas bubble, regardless of the strength of incident shock, shock refraction at the gas bubble surface is regular initially and transforms into the irregular type before the incident shock reaches the top/bottom section of the bubble. In the second study of an underwater explosion near the free surface, the dominant physical phenomena in the earlier stages of explosion consist of the outward propagation of an underwater shock, the symmetrical expansion of a gas bubble and the possible generation of a second shock inside the expanding gas bubble. At a later stage, the underwater shock refraction at the free surface begins resulting in the generation of a pair centered Prandtl–Meyer waves, and the latter interacts with the expanding gas bubble. The numerical results exhibit all the physical phenomena described by Ballhaus and Holt [Phys. Fluids 17 (1974) 1069].

The merging of two gaseous bubbles with an application to underwater explosions

A numerical study of two gaseous bubbles merging into a single coalesced bubble as in underwater explosions is investigated in this paper. This explosive phenomenon is modeled using a boundary integral method. Two configurations, which are in-phase and out-of-phase explosions, are simulated and compared with available experimental results. The thickness of the liquid film between the two bubbles determines our coalescence criterion. Bubble shapes and periods of oscillation are predicted well, compared to those of the experiments.

The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas-gas and gas-water cases

Abstract A technique to simulate the flow field near a moving material interface is developed for multi-material compressible flow, in particular, for compressible gas–water flow. This technique can be conveniently applied with a well-established conservative scheme to solve for the regions away from the interface. Material interfaces are captured using the level set technique with minimum or no smearing. To treat wave interaction with the interface, an implicit characteristic method is developed. In this paper, the method is described in detail and tested extensively for several one-dimensional gas–gas and gas–water cases. Application to multi-dimensional shock–free surface interaction and shock–gas bubble interaction are presented in Part II [Liu TG, Khoo BC, Yeo KS. The simulation of compressible multi-medium flow. Part II: Applications to 2D underwater shock refraction, submitted for publication].

The numerical simulations of explosion and implosion in air : Use of a modified Harten's TVD scheme

Numerical simulations of explosion and implosion in air are carried out with a modified Hartens TVD scheme. The new scheme has a high resolution for contact discontinuities in addition to maintaining the good features of Hartens 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 Hartens TVD scheme for the simulations of shock waves arising from explosion and implosion. Copyright

SIMULATION OF THREE-DIMENSIONAL BUBBLES USING DESINGULARIZED BOUNDARY INTEGRAL METHOD

SUMMARY A very simple model based on the three-dimensional desingularized boundary integral method is applied to study the evolution of bubble(s) with or without the presence of solid structures. The choice of the desingularization parameters, which is crucial to the success of the method, is studied in the context of bubble dynamics. With the proper choice of parameters, the new model is far more efficient than previous models with virtually the same level of accuracy being achieved. This is largely attributed to the simplicity of the desingularization method. Furthermore, the new model offers a simple and attractive way for mesh refinement. Although it has limitations in the sense that, with this model the time stepping tends to slow down as two surfaces approach each other, this can be easily rectified by switching over to a direct method so that the two surfaces can be drawn closer as required in the context of jet impact. After this the new model can be reinstated to treat the complicated doubly connected geometry involving toroidal bubbles that would otherwise be very difficult to deal with. Copyright

Hybridizable discontinuous Galerkin method (HDG) for Stokes interface flow

Abstract In this paper, we present a hybridizable discontinuous Galerkin (HDG) method for solving the Stokes interface problems with discontinuous viscosity and variable surface tension. The jump condition of the stress tensor across the interface is naturally incorporated into the HDG formulation through a constraint on the numerical flux. The most important feature of HDG method compared to other DG methods is that it reduces the number of globally coupled unknowns significantly when high order approximate polynomials are used. For problems with polygonal interfaces, it provides optimal convergence rates of order k + 1 in L 2 -norm for the velocity, pressure and as well as the gradient of velocity. Furthermore, a new approximate velocity can be obtained by an element-by-element postprocessing which converges with order k + 2 in the L 2 -norm. For Stokes interface problems with curved interfaces, we use general curvilinear element to ensure the optimal convergence rates. An error estimate is given for the approximation of the interface. It indicates that curvilinear elements of degree 2 k + 1 should be used for optimal convergence rate of order k + 1 .

The ghost solid method for the elastic solid-solid interface

In this work, three variants of Ghost Solid Method (GSM) are proposed for application to the boundary conditions at the solid-solid interface of isotropic linearly elastic materials, in a Lagrangian framework. It is shown that, in the presence of the wave propagation through the solid-solid mediums, the original GSM [1] can lead to non-physical oscillations in the solution, even for first-order solvers. It is discussed and numerically shown that these oscillations will be more severe if a higher order solver is employed using the original GSM. A scheme for prediction of these non-physical oscillations at the interface is also introduced. The other two variants of GSM proposed, however, can remove the non-physical oscillations that may rise at the interface. Next, the extension to two-dimensional settings with slip and no-slip conditions at the interface is carried out. Numerous numerical examples in one- and two-dimensional settings are provided attesting to the viability and effectiveness of the GSM for treating wave propagation at the solid-solid interface.

The ghost solid methods for the elastic-plastic solid-solid interface and the θ-criterion

Two variants of the Ghost Solid Method (GSM), namely the Original GSM (OGSM) and Modified GSM (MGSM), are proposed for the elastic-plastic solid-solid interactions in a Lagrangian framework. It is shown that the OGSM is highly problem related and can lead to large numerical errors under certain material combinations or in the presence of the wave propagation through the solid-solid interface. The ?-criterion, previously developed for the elastic-elastic solid-solid interactions 1, has been applied to the OGSM for the elastic-plastic interactions. It is shown that this criterion can successfully detect the onset of these large errors. Moreover, it is shown that it can be used to determine the reliability of the results obtained using the OGSM. The MGSM has been shown to be able to remove the large numerical errors that would normally arise due to the OGSM. Next, the extension of the two variants of the GSM, to two-dimensional settings, is presented for two idealized interface conditions, namely the no-slip condition, and the perfect-slip conditions. Numerous numerical experiments are provided attesting to the effectiveness and viability of the GSMs, for simulating wave propagation at the elastic-plastic solid-solid interface. The applicability of the ?-criterion is also studied in the numerical experiments.