{"title":"带有 LST-DG 预测器和后验子单元 ADER-WENO 有限体积限制的时空自适应 ADER-DG 有限元法用于多维爆轰波模拟","authors":"I. S. Popov","doi":"arxiv-2409.09911","DOIUrl":null,"url":null,"abstract":"The space-time adaptive ADER-DG finite element method with LST-DG predictor\nand a posteriori sub-cell ADER-WENO finite-volume limiting was used for\nsimulation of multidimensional reacting flows with detonation waves. The\npresented numerical method does not use any ideas of splitting or fractional\ntime steps methods. The modification of the LST-DG predictor has been\ndeveloped, based on a local partition of the time step in cells in which strong\nreactivity of the medium is observed. This approach made it possible to obtain\nsolutions to classical problems of flows with detonation waves and strong\nstiffness, without significantly decreasing the time step. The results obtained\nshow the very high applicability and efficiency of using the ADER-DG-PN method\nwith a posteriori sub-cell limiting for simulating reactive flows with\ndetonation waves. The numerical solution shows the correct formation and\npropagation of ZND detonation waves. The structure of detonation waves is\nresolved by this numerical method with subcell resolution even on coarse\nspatial meshes. The smooth components of the numerical solution are correctly\nand very accurately reproduced by the numerical method. Non-physical artifacts\nof the numerical solution, typical for problems with detonation waves, such as\nthe propagation of non-physical shock waves and weak detonation fronts ahead of\nthe main detonation front, did not arise in the results obtained. The results\nof simulating rather complex problems associated with the propagation of\ndetonation waves in significantly inhomogeneous domains are presented, which\nshow that all the main features of detonation flows are correctly reproduced by\nthis numerical method. It can be concluded that the space-time adaptive\nADER-DG-PN method with a posteriori sub-cell ADER-WENO finite-volume limiting\nis perfectly applicable to simulating complex reacting flows with detonation\nwaves.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation\",\"authors\":\"I. S. Popov\",\"doi\":\"arxiv-2409.09911\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The space-time adaptive ADER-DG finite element method with LST-DG predictor\\nand a posteriori sub-cell ADER-WENO finite-volume limiting was used for\\nsimulation of multidimensional reacting flows with detonation waves. The\\npresented numerical method does not use any ideas of splitting or fractional\\ntime steps methods. The modification of the LST-DG predictor has been\\ndeveloped, based on a local partition of the time step in cells in which strong\\nreactivity of the medium is observed. This approach made it possible to obtain\\nsolutions to classical problems of flows with detonation waves and strong\\nstiffness, without significantly decreasing the time step. The results obtained\\nshow the very high applicability and efficiency of using the ADER-DG-PN method\\nwith a posteriori sub-cell limiting for simulating reactive flows with\\ndetonation waves. The numerical solution shows the correct formation and\\npropagation of ZND detonation waves. The structure of detonation waves is\\nresolved by this numerical method with subcell resolution even on coarse\\nspatial meshes. The smooth components of the numerical solution are correctly\\nand very accurately reproduced by the numerical method. Non-physical artifacts\\nof the numerical solution, typical for problems with detonation waves, such as\\nthe propagation of non-physical shock waves and weak detonation fronts ahead of\\nthe main detonation front, did not arise in the results obtained. The results\\nof simulating rather complex problems associated with the propagation of\\ndetonation waves in significantly inhomogeneous domains are presented, which\\nshow that all the main features of detonation flows are correctly reproduced by\\nthis numerical method. It can be concluded that the space-time adaptive\\nADER-DG-PN method with a posteriori sub-cell ADER-WENO finite-volume limiting\\nis perfectly applicable to simulating complex reacting flows with detonation\\nwaves.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"3 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09911\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09911","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation
The space-time adaptive ADER-DG finite element method with LST-DG predictor
and a posteriori sub-cell ADER-WENO finite-volume limiting was used for
simulation of multidimensional reacting flows with detonation waves. The
presented numerical method does not use any ideas of splitting or fractional
time steps methods. The modification of the LST-DG predictor has been
developed, based on a local partition of the time step in cells in which strong
reactivity of the medium is observed. This approach made it possible to obtain
solutions to classical problems of flows with detonation waves and strong
stiffness, without significantly decreasing the time step. The results obtained
show the very high applicability and efficiency of using the ADER-DG-PN method
with a posteriori sub-cell limiting for simulating reactive flows with
detonation waves. The numerical solution shows the correct formation and
propagation of ZND detonation waves. The structure of detonation waves is
resolved by this numerical method with subcell resolution even on coarse
spatial meshes. The smooth components of the numerical solution are correctly
and very accurately reproduced by the numerical method. Non-physical artifacts
of the numerical solution, typical for problems with detonation waves, such as
the propagation of non-physical shock waves and weak detonation fronts ahead of
the main detonation front, did not arise in the results obtained. The results
of simulating rather complex problems associated with the propagation of
detonation waves in significantly inhomogeneous domains are presented, which
show that all the main features of detonation flows are correctly reproduced by
this numerical method. It can be concluded that the space-time adaptive
ADER-DG-PN method with a posteriori sub-cell ADER-WENO finite-volume limiting
is perfectly applicable to simulating complex reacting flows with detonation
waves.