The exercise in this course is to analyse a set of mathematical software tools concerning their speed, accuracy and flexibility. For this purpose a known benchmark problem of engineering type is simulated with each software tool and the results are compared with reference values. Our object of investigation is the so-called `flow around a cylinder`-problem, which is widely accepted as standard test for accuracy and performance of mathematical software tools. This problem is a typical test problem for analyzing the behavior of flow behind a rigid body: A circular obstacle is fixed at a special position in a long channel. The obstacle is surrounded by a fluid that is passing through the cylinder.
Depending on the speed of the inflow (or the Reynolds-number, resp.) the flow behind the obstacle shows one of the three prototypical forms of flows: Using a `low` Reynolds-number the flow becomes steady. Using a `mid-range` Reynolds-number the flow becomes unsteady but shows a periodic behavior (the so called `von Karman vortex street`), whereas using `high` Reynolds-number the flow may become completely chaotic. The phenomena of such flow problems are visible everywhere around our living environments such as: flow around high-rise building, the drag force induced by driving car accelerating in the wind, ocean current interaction with the offshore structures, etc. As viewed from engineering, it is important to predict for example the drag- and lift-forces on such an obstacle or the frequency of a vibration at various fluid speeds in order to avoid undesirable resonances in the vibration of the solid structures.
Here we concentrate our investigation on three types of commercial mathematical software tools: FEMLAB, CFX and FLUENT. All three types of software use different mathematical approaches to simulate flow and every software should be able to calculate a more or less accurate solution to the model problem. To be more precise we will concentrate on the following questions:
- How accurate is the solution that can be obtained by a simple modeling?
- How much time will the computation need?
- Is it possible to optimize the results in terms of speed and/or accuracy? What possibilities are offered by the software for doing that?
- Are there any major restrictions or drawbacks in the software? (Only 2D, only 3D, …)
- How easy is it to set up the benchmark configuration in each software product? Is the software easy to handle?