Numerical approaches for computation of fronts

TY - JOUR

T1 - Numerical approaches for computation of fronts

AU - Sheintuch, Moshe

PY - 1990

Y1 - 1990

N2 - Moving fronts and pulses appear in many engineering applications like flame propagation and a falling liquid film. Standard computation methods are inappropriate since the problem is defined over an infinite domain and a steady‐state solution exists only for a certain front velocity. This work presents a transformation that converts the original problem into a boundary‐value problem within a finite domain, in a way that preserves the behavior at the boundaries. Good low‐order approximations can be obtained as demonstrated by two examples. In another approach, a central element of adjustable length is incorporated into a three‐element structure where the edge‐elements obey known asymptotic solutions. That yields multiplicity of travelling fronts in an infinite domain but it successfully approximates standing wave solutions in a finite domain. The approximate solutions are shown to obey the qualitative features known for the exact solutions, like asymptotic solutions or the bifurcation set–the boundary where a new solution emerges or disappears.

AB - Moving fronts and pulses appear in many engineering applications like flame propagation and a falling liquid film. Standard computation methods are inappropriate since the problem is defined over an infinite domain and a steady‐state solution exists only for a certain front velocity. This work presents a transformation that converts the original problem into a boundary‐value problem within a finite domain, in a way that preserves the behavior at the boundaries. Good low‐order approximations can be obtained as demonstrated by two examples. In another approach, a central element of adjustable length is incorporated into a three‐element structure where the edge‐elements obey known asymptotic solutions. That yields multiplicity of travelling fronts in an infinite domain but it successfully approximates standing wave solutions in a finite domain. The approximate solutions are shown to obey the qualitative features known for the exact solutions, like asymptotic solutions or the bifurcation set–the boundary where a new solution emerges or disappears.

UR - http://www.scopus.com/inward/record.url?scp=84985304768&partnerID=8YFLogxK

U2 - 10.1002/num.1690060104

DO - 10.1002/num.1690060104

M3 - 文章

AN - SCOPUS:84985304768

SN - 0749-159X

VL - 6

SP - 43

EP - 58

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 1

ER -