A historical oversight: Vladimir P. Kolgan and his high-resolution scheme

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Abstract

The Russian landmark paper “Application of the principle of minimizing the derivative to the construction of finite-difference schemes for computing discontinuous solutions of gas dynamics” by Vladimir P. Kolgan is discussed in a historical–technical perspective. The 1972 paper already featured a Godunov-type scheme for the Euler equations with second-order spatial accuracy, and a limiter to make it monotonicity-preserving. The work remained little known within and completely unknown outside the USSR, largely because of Kolgan’s untimely death in 1978. To honor Kolgan’s contribution to CFD, an English translation of his paper is included in this issue of the Journal of Computational Physics. Facts about Kolgan’s life are presented here, and an appraisal is given of the originality of his ideas.

Introduction

This article is meant as a historical and technical commentary to the article immediately following it: the 1972 research paper “Application of the principle of minimizing the derivative to the construction of finite-difference schemes for computing discontinuous solutions of gas dynamics” by Vladimir P. Kolgan. The article originally appeared in Russian in the TsAGI Research Notes 3 (1972) 68–76, and is a true milestone in the history of CFD. It was translated by Konstantin Kabin and Valeriy Tenishev for publication in the Journal of Computational Physics. The reasons for reprinting this article in the English language will be made clear in the present article.

Section snippets

The birth of high-resolution scheme

Computational Fluid Dynamics (CFD) owes its present success to a large degree to the advent of the so-called high-resolution (HR) schemes [1] 40 years ago. Such schemes are at least second-order accurate in regions where the flow solution is smooth, while capturing discontinuities as narrow, monotone structures.

For an appreciation of the problem of designing a high-resolution scheme for the Euler equations it is useful to first consider modeling the linear advection of a step function. Here we

An interrupted life

The most obvious reason for Kolgan’s lack of influence is his untimely death: he succumbed to lung cancer in 1978, at the age of 37. At that time the final papers by Boris’ group and by Van Leer had yet to appear.

Other circumstances may have contributed, in particular, the relative isolation of Kolgan’s place of employment. The research environment at TsAGI was industrial rather than academic. Dr. Vladimir Yumashev of TsAGI, a former collaborator of Kolgan, sent me an all-too-familiar story

The 1972 TsAGI paper

In this issue of JCP you will find an English translation of Kolgan’s 1972 TsAGI paper [5], describing his non-oscillatory Godunov-type method of second spatial and first temporal order of accuracy. Its title is: “Application of the principle of minimizing the derivative to the construction of finite-difference schemes for computing discontinuous solutions of gas dynamics.” The paper is straightforward; I will restrict myself to pointing out the significance of Kolgan’s findings.

I have

In search of Kolgan: a personal account

At the start of 1978 I was done with the writing of the series “Towards the Ultimate Conservative Difference Scheme.” I had submitted the last paper, “A Second-Order Sequel to Godunov’s Method,” to the Journal of Computational Physics in October 1977 and was waiting for the reviews to come in. I had explicitly asked the editor of JCP “to include a Soviet scientist among the referees.” I could well imagine that some little-known scientist in the USSR was ahead of me, and I wanted to do the best

Epilogue

My paper on the sequel to Godunov’s method appeared in 1979. A year later I met Rusanov at an international conference and learned he had been my Russian reviewer. He then shared with me a curious memory from the 1960s when he and Godunov still worked at the same institute. At that time Godunov actually discouraged Rusanov from trying to find a higher-order extension of his method, because he believed it was a unique, isolated method, one without a sequel. This could explain in part why in

Acknowledgements

The author is indebted to Dr. Vladimir Sabel’nikov for providing the 1972 Kolgan paper and continued interest in the “Kolgan Project;” furthermore, to Dr. Vladimir Yumashev for providing detailed information about Kolgan’s life and work. He also thank Dr. Valeriy Tenishev for unlocking Kolgan’s article with a rough translation, and Dr. Konstantin Kabin for providing the fine final translation. Without the interest of these people this project would not have been.

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