• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.655-681
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• 1998

Discontinuous solutions or interfaces are common in nature, for examples, shock waves or material interfaces. However, their numerical computation is difficult by the feature of discontinuities. In this paper, we summarize the numerical approaches for discontinuities and interfaces appearing mostly in the system of hyperbolic conservation laws, and explain various numerical methods for them. We explain two numerical approaches to handle discontinuities in the solution: shock capturing and shock tracking, and illustrate their underlying algorithms and mathematical problems. The front tracking method is explained in details and the level set method is outlined briefly. The several applications of front tracking are illustrated, and the research issues in this field are discussed.

• International Journal of Aeronautical and Space Sciences
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• v.12 no.3
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• pp.211-224
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• 2011

This is a written version of an hour-long lecture delivered by the author on June 30, 2011, as Plasmadynamics and Lasers Award Lecture at the AIAA 2011 summer conference in Honolulu, Hawaii. The author proposes that two areas of planetary entry physics be pursued in the future: outer planet aero-capturing and study of aerodynamics of meteoroid entries, both for the purpose of advancing the understanding of the possible extraterrestrial seeding of building blocks of life. For outer planet aero-capturing, the author proposes to develop new shock tube facilities that will produce up to 30 km/s of shock speed without causing photo-ionization of the driven gas by the radiation from the hot driver gas. Regarding meteors, the author proposes to carry out laboratory testing of the Tunguska event and of the seeding of amino acid molecules using a ballistic range which shoots a snowball laden with amino acid molecules toward a water surface.

• 한국전산유체공학회:학술대회논문집
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• 2002.10a
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• pp.103-108
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• 2002

The M-AUSMPW+ scheme that can capture shock waves exactly with monotonic characteristics is modifided from AUSMPW+ by analyzing the cause of oscillation in shock regions. Firstly shock-capturing characteristics of general FVS including the AUSM-type schemes are investigated in detail, according to the difference between a cell-interface and a sonic transition position. The cause of oscillation is the improper numerical dissipation that could not represent the real Physics. The M-AUSMPW+ could capture shocks exactly without oscillatory behaviors in considering the sonic transition position and an cell-interface position.

• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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• pp.11-19
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• 2001

An adaptive nonlinear artificial dissipation model is presented for performing aeroacoustic computations by the high-order and high-resolution numerical schemes based on the central finite differences. An effective formalism of it is devised by combining a selective background smoothing term and a well-established nonlinear shock-capturing term which is for the temporal accuracy as well as the numerical stability. A conservative form of the selective background smoothing term is presented to keep accurate phase speeds of the propagating nonlinear waves. The nonlinear shock-capturing term that has been modeled by the second-order derivative term is combined with it to improve the resolution of discontinuities and stabilize the strong nonlinear waves. It is shown that the improved artificial dissipation model with an adaptive control constant which is independent of problem types reproduces the correct profiles and speeds of nonlinear waves, suppresses numerical oscillations near discontinuity and avoids unnecessary damping on the smooth linear acoustic waves. The feasibility and performance of the adaptive nonlinear artificial dissipation model are investigated by the applications to actual computational aeroacoustics problems.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.126-127
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• 2003

In the generalized characteristic coordinate system (GCCS) proposed by Wu and Shi [1], the frame moves at a speed which is a linear combination of the convective speed and the sound speed, thus unifying the classical Eulerian approach, Lagrangian approach, and the unified coordinate system (UCS) of Hui and his co-workers [2]. Here some properties of Euler equations in the GCCS are studied and the advantages of GCCS in capturing expansion fans and shock waves are demonstrated by the results of numerical tests.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.39-44
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• 2000

Two-dimensional Navier-Stokes codes are used to simulate the shock tunnel in Konkuk university. In order to design experiments in impulse facilities properly and to interpret data from such facilities, it is necessary to understand how the flow approaches steady state. This is done by determining the transient flow field and flow establishment time around a given model. This will be accomplished by developing appropriate CFD codes which solve the Navier-Stokes equations, and simulating the starting process and resulting unsteady viscous flow phenomena. The starting process in a shock tunnel consists of multiple shock interactions and contact discontinuities, which are difficult to solve with the classical shock capturing schemes. A recently developed high resolution scheme is adapted for resolving the unsteady phenomena of those multiple shock interactions and contact surfaces during the starting process. The bifurcation phenomenon due to the interactions of the reflected shock from the end of the shock tube with the boundary layer generated by the incident shock becomes of particular interest. By comparing with the experiment results, the accuracy of the numerical analysis is validated and it is demonstrated that the properties which can hardly be obtained through the experiment can be estimated.

• Journal of computational fluids engineering
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• v.12 no.1
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• pp.60-67
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• 2007

In this paper, the dispersion controlled dissipative (DCD) scheme is reviewed and then extended to simulate chemically reacting gas flows in multicomponent mixtures in the presence of strong shock waves. Furthermore, the properties of the reactive DCD (DCD-R) scheme are discussed, followed by several applications. The DCD scheme has been shown to have the following features: high accuracy and robustness for reacting gas flows in the presence of strong shock waves and contact discontinuities, and algorithmic simplicity.

• Advances in aircraft and spacecraft science
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• v.7 no.5
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• pp.387-404
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• 2020

The numerical simulation of shock waves in supersonic flows is challenging because of several instabilities which can affect the solution. Among them, the carbuncle phenomenon can introduce nonphysical perturbations in captured shock waves. In the present work, a hybrid numerical flux is proposed for the evaluation of the convective fluxes that avoids carbuncle and keeps high-accuracy on shocks and boundary layers. In particular, the proposed flux is a combination between an upwind approximate Riemann problem solver and the Local Lax-Friedrichs scheme. A simple strategy to mix the two fluxes is proposed and tested in the framework of a discontinuous Galerkin discretisation. The approach is investigated on the subsonic flow in a channel, on the supersonic flow around a cylinder, on the supersonic flow on a flat plate and on the flow in a overexpanded rocket nozzle.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.2
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• pp.30-38
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• 2002

The monotonic characteristics of AUSM-type shemes are proven by mathmatics and numerics. Qualitatively well-known characteristics are quantified by mathematics and the magnitude of oscillatory behaviors of each schemes could be compared directly. Moreover, it is also studied how the sonic transition position affects the oscillation in capturing the shocks. Lastly M-AUSMPW+, the latest improved AUSM-type scheme, is shown to have monotonic characeristics though all shock conditions.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.112-122
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• 1996

A finite element scheme using the concept of PISO method has been developed to solve the Navier-Stokes viscous flows in all speed range. This scheme includes development of new pressure equation that retains both the hyperbolic term related with the density variation and the elliptic term reflecting the incompressibility constraint. The present method is applied to the incompressible two-dimensional driven cavity flow problems(Re=100, 400 and 1,000). For compressible flows, the Carter plate problem(M=3 and Re=1,000) is computed. Finally, we have simulated the shock-boundary layer interaction(M=2 and Re=2.96×10/sup 5/), a more difficult problem, and compared its results with the experiment to demonstrate the shock capturing capability of the present solution algorithm.