Basic function scheme of polynomial type

A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.

The Character and Petrogenetic Model of the Permian Tarim Large Igneous Province

Tarim Large Igneous Province(TLIP)is the second Late Paleozoic LIPs in China after the recognition of the Emeishan LIP.The residual distribution range of TLIP is up to 250000 km2,and the largest residual thickness is 780 m.The eruption of basalt happened during 290–288 Ma and belongs to LIPs magmatic event with fast eruption of magma.The lithological units of the TLIP include basalt,diabase,layered intrusive rock,breccia pipe mica-olivine pyroxenite,olivine pyroxenite,gabbro,ultramafic dyke,quartz syenite,quartz syenite porphyry and bimodal dyke.The basalt and diabase of TLIP exhibit OIB-like trace element patterns and enrichment of LILE and HFSE,and mainly belong to high TiO2 series.There is an obvious difference in isotope among the basalt from Keping and the basalt and dibase from the northern Tarim Basin.The basalt from Keping with negative Nd and high REE value derives from enriched mantle,and the diabase and basalt from the northern Tarim Basin with positive Nd and low REE value are related to depleted mantle.The crust uplifting in the Early Permian and the development of picrite and large scale dyke and formation of large scale V-Ti-magnetite deposit in Wajilitag area support the view that the TLIP is related to mantle plume.The TLIP has a temporal-spatial relationship with Permian basicultrabasic igneous rock,which is distributed widely in Central Asia,and they represent a tectono-magmatic event with very important geodynamic setting.This study also systematically demonstrates the two-stage melting model for the TLIP based on our previous research work and predecessor achievements,and highlights the two types of magmatic rocks within the TLIP.The two-stage melting model suggests that the formation of the TLIP is mantle plume related.The early hot mantle plume caused the low-degree partial melting of the lithosphere mantle,while in the later stage,the plume partially melted due to adiabatic uplift and decompression.Therefore,this model carries signatures of both the"Parana"and"Deccan"models in terms of mantle plume activity.During the early stage,the mantle plume provided the heat required for partial melting of sub-continental lithosphere mantle(SCLM),similar to the"Parana Model",while later the plume acted as the main avenue for melting,as in the"Deccan Model".Basalts that erupted in the first stage have higher 87Sr/86Sr,lower 143Nd/144Nd ratios,and are enriched in large ion lithophile elements and high field strength elements,indicating a possible origin from the enriched continental lithosphere mantle,similar to the Parana type geochemical features.The basic-ultrabasic intrusive rocks in the second stage exhibit lower 87Sr/86Sr,higher 143Nd/144Nd ratios relative to the basalts,consistent with the involvement of a more depleted asthenospheric material,such as a mantle plume,similar to the Deccan type geochemical features.The first stage basalts can be further subdivided into two categories.Developing this petrogenetic model for the TLIP aids in comprehensively understanding its magmatism and deep geological and geodynamic processes.Furthermore,this work enriches the theories describing the origin of large igneous province and mantle plume activity.