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Highly Accurate Compressible Fluid solver

In flu­id me­chan­ics, the flow is con­sid­ered com­press­ible when the flu­id den­si­ty varies sig­nif­i­cant­ly in re­sponse to a change in pres­sure. Com­press­ibil­i­ty ef­fects are typ­i­cal­ly con­sid­ered sig­nif­i­cant if the Mach num­ber (the ra­tio of the flow ve­loc­i­ty to the lo­cal speed of sound) of the flow ex­ceeds 0.3, or if the flu­id un­der­goes very large pres­sure changes. The most dis­tinct phe­nom­e­non as­so­ci­at­ed with high speed flows is the ex­is­tence of non isen­trop­ic so­lu­tions or shock waves.

The new com­press­ible solver in­tro­duced in LS-DY­NA is based on the space-time con­ser­va­tion el­e­ment and so­lu­tion el­e­ment (CE/­SE) method, orig­i­nal­ly pro­posed by Dr. Chang in NASA Glenn Re­search Cen­ter. It is a new nu­mer­i­cal frame­work for solv­ing con­ser­va­tion laws. The CE/­SE method is not an in­cre­men­tal im­prove­ment of a pre­vi­ous­ly ex­ist­ing CFD method, and it dif­fers sub­stan­tial­ly from many oth­er well-es­tab­lished meth­ods. The CE/­SE method is a sec­ond or­der ex­plic­it scheme  and it has many non­tra­di­tion­al fea­tures. Some of the most im­por­tant fea­tures in­clude :

  • The flux con­ser­va­tion in space AND time (lo­cal­ly and glob­al­ly) that al­lows a phys­i­cal re­al­i­ty to be re­tained even in re­gions of dis­con­ti­nu­ities.
  • The spa­tial de­riv­a­tives are treat­ed as un­knowns rather then dis­cretized which al­lows high­ly ac­cu­rate so­lu­tions (more ac­cu­rate than nor­mal sec­ond or­der schemes).
  • A  nov­el and ef­fi­cient shock cap­tur­ing strat­e­gy that does not use clas­sic Rie­mann solvers.
  • Flex­i­ble el­e­ment shape (e.g., hexa­he­dra, wedges, tetra­he­dra, ... ).
  • Both strong shocks and small dis­tur­bances can be han­dled very well si­mul­ta­ne­ous­ly.

To date, this method has been used to solve many dif­fer­ent types of flow prob­lems, such as det­o­na­tion waves, shock/­acoustic wave in­ter­ac­tion, cav­i­tat­ing flows, and chem­i­cal re­ac­tion flows.