isothermal shock problems]{}]{}[^4]'
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Detonation waves – Gas dynamics – General fluid mechanics – Low-dimensional models – Shock waves

76L05 35L67 34A36 85A30 76M55

Introduction
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Strong one-dimensional (1D) point-like explosions have been investigated thoroughly since the pioneering work of [@Sedov1946; @Taylor1950]. Shock waves arising by reflection of a fluid on a solid wall were studied by Noh [@Noh1987]. Meyer [@Meyer1988] used Nohs solution for code verification whereby he also confirmed his findings with experimental data. Gehmeyr [@Gehmeyr1997] enhanced Nohs implosion problem (IP) by giving analytical solutions to $n$ shock reflections on rigid walls on both sides of a tube. Since decades, these solutions are used for testing CFD codes because resolving shock waves is a crucial feature for verifying conservation properties of inviscid, compressible fluids. Moreover, Sedovs explosion problem (EP) is still in use for simple modelling of Supernova Remnants (SNR) [@Allen2014; @Leahy2016; @Lerche1976; @Solinger1975] in their early evolutionary states [@Vink2012; @Woltjer1972].

Almost all previous works considered energy conservation with an ideal gas equation of state. To the authors knowledge, the IP was never considered to be isothermal. In case of the EP an unphysical diverging temperature gradient behind the shockwave [@Sedov1959; @Solinger1975] occurs. Referring to this, Korobeinikov [@Korobeinikov1956; 