Efficient and Reliable Integration Methods for Particle Tracing in Unsteady Flows on Discrete Meshes
In real applications the velocity field of a flow is not available in analytical but in discrete form. One goal of this paper is to analyze particle integration methods for discretized data defined on meshes with regard to numerical efficiency and accuracy. Careful error analysis of the particle tracing process relates the error of velocity interpolation in space and time to the error of the numerical integration. Hence, a fast integration routine which provides accuracy similar to that of interpolation is necessary. This leads to a robust integration routine with adaptive step size control and error monitoring. A second aspect of this work is the treatment of stiff problems. Stiffness occurs m flows with strong shear deformations or vorticity. To detect stiffness in a given flow field, the Jacobian of the velocity field is analyzed. Implicit integration methods are used to handle stiff systems of ordinary differential equations.
KeywordsVelocity Field Stiff System Implicit Algorithm High Order Algorithm Implicit Integration Method
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