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Dynamics of Two-Phase Flows

ISBN Druckformat: 0-8493-9925-4



A discussion is given of discrete modeling considerations in multiphase fluid dynamics and related areas. By the term "discrete modeling" we refer to a collection of ideas and concepts which we hope will ultimately provide a philosophical basis for a more systematic approach to the solution of practical engineering problems using digital computers. Our conception of discrete modeling is still evolving and has not yet led to useful results; thus the present paper is of the nature of a preliminary report on work in progress, and its primary purpose is to stimulate further thought and discussion. As presently constituted, the main ingredients in our discrete modeling Weltanschauung are the following considerations: (1) Any physical model must eventually be cast into discrete form in order to be solved on a digital computer. (2) The usual approach of formulating models in differential form and then discretizing them is an indirect route to a discrete model. It is also potentially hazardous: the length and time scales of the discretization may not be compatible with those represented in the model. It may therefore be preferable to formulate the model in discrete terms from the outset. (3) Computer time and storage constraints limit the resolution that can be employed in practical calculations. These limits effectively define the physical phenomena, length scales, and time scales which cannot be directly represented in the calculation and therefore must be modeled. This information should be injected into the model formulation process at an early stage. (4) Practical resolution limits are generally so coarse that traditional convergence and truncation-error analyses become irrelevant. (5) A discrete model constitutes a reduced description of a physical system, from which fine-scale details are eliminated. This elimination creates a closure problem, which has an inherently statistical character due to uncertainty about the missing details. Methods from statistical physics may therefore be useful in the formulation of discrete models. In the present paper we elaborate on these themes and illustrate them with simple examples.
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