{"title":"Modelling of stellar convection.","authors":"Friedrich Kupka, Herbert J Muthsam","doi":"10.1007/s41115-017-0001-9","DOIUrl":"10.1007/s41115-017-0001-9","url":null,"abstract":"<p><p>The review considers the modelling process for stellar convection rather than specific astrophysical results. For achieving reasonable depth and length we deal with hydrodynamics only, omitting MHD. A historically oriented introduction offers first glimpses on the physics of stellar convection. Examination of its basic properties shows that two very different kinds of modelling keep being needed: low dimensional models (mixing length, Reynolds stress, etc.) and \"full\" 3D simulations. A list of affordable and not affordable tasks for the latter is given. Various low dimensional modelling approaches are put in a hierarchy and basic principles which they should respect are formulated. In 3D simulations of low Mach number convection the inclusion of then unimportant sound waves with their rapid time variation is numerically impossible. We describe a number of approaches where the Navier-Stokes equations are modified for their elimination (anelastic approximation, etc.). We then turn to working with the full Navier-Stokes equations and deal with numerical principles for faithful and efficient numerics. Spatial differentiation as well as time marching aspects are considered. A list of codes allows assessing the state of the art. An important recent development is the treatment of even the low Mach number problem <i>without</i> prior modification of the basic equation (obviating side effects) by specifically designed numerical methods. Finally, we review a number of important trends such as how to further develop low-dimensional models, how to use 3D models for that purpose, what effect recent hardware developments may have on 3D modelling, and others.</p>","PeriodicalId":74085,"journal":{"name":"Living reviews in computational astrophysics","volume":"3 1","pages":"1"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6319542/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36870737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics.","authors":"José María Martí, Ewald Müller","doi":"10.1007/lrca-2015-3","DOIUrl":"https://doi.org/10.1007/lrca-2015-3","url":null,"abstract":"<p><p>An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution of the Riemann problem in RMHD, and to simulate 1D RMHD flows in Cartesian coordinates.</p><p><strong>Electronic supplementary material: </strong>Supplementary material is available for this article at 10.1007/lrca-2015-3.</p>","PeriodicalId":74085,"journal":{"name":"Living reviews in computational astrophysics","volume":"1 1","pages":"3"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/lrca-2015-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36870736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"SPH Methods in the Modelling of Compact Objects","authors":"S. Rosswog","doi":"10.1007/lrca-2015-1","DOIUrl":"https://doi.org/10.1007/lrca-2015-1","url":null,"abstract":"","PeriodicalId":74085,"journal":{"name":"Living reviews in computational astrophysics","volume":"1 1","pages":"1-109"},"PeriodicalIF":0.0,"publicationDate":"2014-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/lrca-2015-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51700803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}