A temporal multi-scale algorithm for efficient fluid modeling of a one-dimensional gas discharge

In this study, we present a temporal multi-scale algorithm (TMA) for efficient fluid modeling of a one-dimensional gas discharge with complex plasma chemistry. A helium dielectric barrier discharge driven by a power source with a frequency of 25 kHz is used as an example to demonstrate the superior capability of the TMA in accelerating fluid modeling simulations, while maintaining the same accuracy as compared to lengthy benchmarking fluid modeling using a single time-scale approach. The plasma chemistry considers 36 species and 121 reaction channels, which include some impurities such as nitrogen (25 ppm), oxygen (10 ppm) and water vapor (1 ppm), in addition to the helium itself. The results show that the runtime using the TMA can be dramatically reduced to 4% (25 times faster) with a relative difference of spatially averaged number densities generally less than 1% for all species between the TMA and the benchmarking cases when five initial cycles, five supplementary cycles and four repeated stages are used. Further reduction of the accuracy requirements to 44% for some specific species can lead to 92 times faster performance with the use of two initial cycles, two supplementary cycles and two repeated stages. The outlook for multi-dimensional fluid modeling considering a gas flow field is also described at the end of the paper.