Reduced-order modeling - New approaches for computational physics

111 this paper, we rcvicw the deve lo l~n~e~~ t of new reducecl-orcler ~ r ~ o t l e l i ~ ~ g tecl~niques ant1 tliscuss their applicalrility to variolts prol)len~s in co~ril)utatior~ul pl~ysics. Eu~pllasis is gi~.cn to r~~ctho(ls basetl 011 j'olterra series re l ) rese~~ta t io~~s and thr proper ortllogo11a1 deco~~~position. Results are reported for cliffcre~~t 11ol11i11ear systct~l~s to 1)rovidc clear cxan~ples of the cor~struc.tio~~ a11t1 usc of recluc~cd-orcler llod(>ls, p;lrtic.ularly ill the 1l11tlti-cliscil)li11:1ry field of c o ~ ~ ~ l ) u t a t i o ~ ~ a l aeroelasticity. U~~s t eady aerodj,nan~ic and aeroelast,ic behaviors of two-di~nrnsional and three-dinle~~sional geo~~~e t r i e s arc. tlcscri1)etl. Large illcreases in co1111)utational efficie~~c,y are ol~t,:ii~lccl thruugl~ the use of rcducetl-order ~r~otlc!ls! thcrebj. justifying the izlitial c.onlputatio11a1 esl)c:~~se of constructing th(:sr r~~oticls and ~ ~ ~ o t i v a t i r ~ g tl~eirusc for ~~~ult i-disc, i[)I i~la~>. design analysis.