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Based on a Riemann solver adaptive mesh refinement code, we present a model, which fulfills the basic requirements of running it sufficiently long in order to erase memory effects of the initial conditions, set up a disk\u2010halo fountain flow cycle, for converging solutions with increasing mesh refinement. We obtain the following results: (i) in a supernova driven ISM, high Reynolds number turbulence generates structures on all scales, (ii) the volume filling factor of the hot gas is substantially reduced due to the fountain flow, (iii) gas clouds are transient shock compressed layers, (iv) more than half of the gas mass resides in thermally unstable regimes, (v) O VI is distributed in patchy mixing layers, with the derived column densities being in agreement with FUSE and Copernicus observations, (vi) the electron density distribution up to distances of 8 kpc in the disk is consistent with pulsar dispersion measure observations, provided that the electron and ionization structure are not in equilibrium, (vii) the interstellar cooling function depends both on <jats:italic>space and time<\/jats:italic> (and not only on temperature and metallicity), (viii) the Local Bubble has been produced by 14\u201320 supernovae about 14 Myr ago, exploding in a moving group on its path through the local ISM, (ix) the nearest supernova explosion to Earth occurred 2.2 \u00d7 10<jats:sup>6<\/jats:sup> yr ago at a distance of \u223c85 pc, in agreement with measurements of the radionuclide <jats:sup>60<\/jats:sup>Fe found in the ferromanganese crust on the ocean floor (\u00a9 2012 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/asna.201211692","type":"journal-article","created":{"date-parts":[[2014,10,15]],"date-time":"2014-10-15T14:53:14Z","timestamp":1413384794000},"page":"486-496","source":"Crossref","is-referenced-by-count":17,"title":["Interstellar medium simulations"],"prefix":"10.1002","volume":"333","author":[{"given":"D.","family":"Breitschwerdt","sequence":"first","affiliation":[]},{"given":"M.A.","family":"de Avillez","sequence":"additional","affiliation":[]},{"given":"J.","family":"Feige","sequence":"additional","affiliation":[]},{"given":"C.","family":"Dettbarn","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,6,18]]},"reference":[{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1745-3933.2008.00526.x"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1051\/0004-6361:20020627"},{"key":"e_1_2_1_4_1","first-page":"3","volume":"217","author":"Bower C.S.","year":"1968","journal-title":"Nature"},{"key":"e_1_2_1_5_1","unstructured":"Breitschwerdt D. de Avillez M.A.:2007 in: B.G. 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