Overture plays on methods for faster, more accurate models

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It’s in the formulas

Complex formulas called partial differential equations (PDEs) mathematically describe the continuous processes, like combustion, that Henshaw’s tools model.  PDEs are the core of many simulations, but computers can’t solve them until the PDEs are approximated by algebraic equations at discrete data points.

The data points are distributed in a grid or mesh pattern throughout the area in which a process, such as fluid flow, is being modeled.  The computer calculates what’s happening to pressure, velocity, temperature and other properties at each one of the data points as the simulation progresses.

Taken together, the points portray what’s happening.  The closer together the points are, the more precise the model is – and the more computer power it demands.

The right mesh or grid is critical to finding a solution quickly and accurately, Henshaw says.

“You want [the grid] to have very nice properties, because it makes the rest of your problem easier,” he adds.  But as problems change, such as when modeling moving objects, “then this fundamental structure has to change; this grid has to change.”

For some solution techniques, changing creates big demands for computer resources, Henshaw says.  The computer must regenerate the grids while retaining all the right properties, such as well-distributed data points.  In some cases, the grids may become tangled.

In other methods, the algorithm may be precise and fast, but may require time and resources to start.  Restructuring the grid means reinitializing the problem, which causes delays and demands resources, Henshaw says.

“You need to have methods that have low startup. … The job is to come up with algorithms that allow you to do that,” Henshaw says.  For instance, his group’s methods keep high-quality grids, but change them only where needed to capture important phenomena, like at the boundary between an object and the shock wave or fluid encountering it.

“The approaches we use are very efficient at both allowing you to rapidly change the geometry, but also to keep a nice underlying structure,” he adds.

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