Solution of two‐dimensional multi‐interface Stefan problem by the method of dynamic adaptation

Abstract

In the present work a method of numerical solution of multi‐interface two‐dimensional Stefan problem with explicit tracking of the interfaces in the domains of arbitrary form is considered. The method is based on the idea of dynamic adaptation of the calculated grid by means of transition to an arbitrary non‐stationary coordinate system. The coordinate system transformation is controlled by the solution. The method is described by using the example of the problem that is typical for treatment of materials with concentrated energy fluxes.

Straipsnyje nagrinejamas dvimačio daugiasluoksnio Stefano uždavinio adaptyvus sprendimo algoritmas. Naudojamas išreikštinis fronto skaičiavimo algoritmas, leidžiantis rasti bet kokios formos kontūrus. Remiantis dinaminiu adaptavimo algoritmu, fizine sritis yra atvaizduojama i fiksuota skaičiavimo sriti. Transformacijos atvaizdavimas adaptyviai priklauso nuo pačio uždavinio sprendinio. Bendrasis metodas pateiktas dvieju medžiagu saveikos uždaviniui. Naujojo algoritmo efektyvumas iliustruojamas skaičiavimo eksperimento rezultatais.