Abstract. We present an algorithm for the construction of locally adapted conformal tetrahedral meshes. The algorithm is based on bisection of tetrahedra. A new data structure is introduced, which simplifies both the selection of the refinement edge of a tetrahedron and the recursive refinement to conformity of a mesh once some tetrahedra have been bisected. We prove that repeated application of the algorithm leads to only finitely many tetrahedral shapes up to similarity, and we bound the amount of additional refinement that is needed to achieve conformity. Numerical examples of the effectiveness of the algorithm are presented.

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In this work, we investigate a mathematical model of a spray combustion problem and we prove an existence and uniqueness result for the time-dependent problem. We consider the vaporization of a polydisperse fuel spray of droplets in an oxidative medium, and we assume that the evaporated fuel is immediately consumed and gives off heat. The mathematical model arising from this combustion problem is a coupled system of three partial differential equations. By using the standard method of successive approximations we prove that the system has a unique solution. Moreover, we prove the existence of a front of vaporization, and we show that the mass rate of evaporated droplets decreases when the size of droplets increases.

Wir betrachten ein System von Gleichungen in einer Raumdimension, das die Verbrennung eines Tröpfchen‐Sprays in einer laminaren Gegenströmung beschreibt. Das mathematische Modell wird entwickelt und die Existenz und Eindeutigkeit einer Lösung mil Hilfe einer klassischen Fixpunktmethode bewiesen. Wir geben eine Beschreibung des asymptotischen Verhaltens in der Zeit (das das Löschen der Flamme darstellt) unter gewissen Bedingungen an die physikalischen Parameter. Der Einfluß des mittleren Tröpfchen‐Radius wird untersucht.

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