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SPH & ISPG for Flu­id, Struc­ture, & FSI Problems


  • Jingx­i­ao Xu, Ph.D.
  • Xi­aofei Pan, Ph.D.

SPH & ISPG for Flu­id, Struc­ture, & FSI Problems


This course overviews the SPH and ISPG for­mu­la­tions. We will dis­cuss the the­o­ret­i­cal back­ground and im­ple­men­ta­tion. We will al­so present the lat­est de­vel­op­ments in­clud­ing cou­pling these meth­ods with the La­grange for­mu­la­tion in LS-DY­NA®. We will al­so em­pha­size the ad­van­tages and dis­ad­van­tages of these meth­ods and the suit­abil­i­ty of these meth­ods for var­i­ous ap­pli­ca­tions, in­clud­ing flu­id and sol­id sim­u­la­tions. We will give de­tailed de­scrip­tions of the da­ta re­quired to run LS-DY­NA analy­ses. Ex­am­ples il­lus­trate points made in the lec­ture.


SPH Formulation Fundamentals

  • His­to­ry of the method
    • Vari­able smooth­ing length
    • Dif­fer­ent SPH for­mu­la­tions
  • Spa­tial dis­cretiza­tion of con­tin­u­um equa­tions
    • Char­ac­ter­is­tic lengths
  • Ker­nel func­tions, Method con­sis­ten­cy, Con­cept of renor­mal­iza­tion
  • La­grangian/­Euler­ian forms of SPH & SPH/­La­grangian Cou­pling
  • Ther­mal for­mu­la­tions for SPH
    • Ther­mal cou­pling op­tions be­tween SPH and sol­id parts
  • Mul­ti­ple cou­pling op­tions (in­ter­ac­tion meth­ods) be­tween:
    • Dif­fer­ent SPH parts
    • SPH par­ti­cles & sol­id el­e­ments or oth­er par­ti­cle meth­ods (such as SPG, DEM, Peri­dy­nam­ics)

Implicit SPG Formulation Fundamentals

  • Im­plic­it SPG for­mu­la­tion
    • Spa­tial dis­cretiza­tion
    • Mo­men­tum con­sis­ten­cy
    • Sec­ond-or­der pro­jec­tion scheme
    • Pres­sure Pois­son equa­tion
  • Cou­pling be­tween fi­nite el­e­ment and SPG el­e­ment for con­tact mod­el­ing
  • Sur­face ten­sion mod­el

Examples of SPH & SPH/Lagrangian Coupling

  • Gen­er­al ca­pa­bil­i­ties/­ap­pli­ca­tions (solids & flu­ids)
  • De­tails of an ex­am­ple
    • Con­trol in­put
    • Ma­te­r­i­al
    • Sec­tions
    • Parts
    • Out­put
  • Bound­ary Con­di­tions
  • Con­tacts
  • SPH/­La­grangian Cou­pling Op­tions
  • Ther­mal op­tions for SPH
  • In­ter­ac­tion op­tions be­tween two SPH parts and be­tween SPH and oth­er par­ti­cle meth­ods (such as DEM, SPG)
  • Cre­ation & vi­su­al­iza­tion of SPH par­ti­cles us­ing LS-Pre­Post®

Examples of ISPG

  • Gen­er­al ca­pa­bil­i­ties/­ap­pli­ca­tions
  • De­tails of an ex­am­ple
    • Con­trol In­put
    • Ma­te­r­i­al
    • Sec­tions
    • Parts
    • Out­put
  • Bound­ary con­di­tions
  • Con­tacts
  • LS-Pre­Post & in­put decks