Verification and validation of the open-source plasma fluid code: Zapdos

Corey DeChant, Casey Icenhour, Shane Keniley, Grayson Gall, Alexander Lindsay, Davide Curreli, Steven Shannon

Research output: Contribution to journalArticlepeer-review


Zapdos is an open-source finite element plasma fluid solver based on the MOOSE multiphysics framework. This paper outlines Zapdos verification, benchmarking, and validation efforts for 1D and 2D RF capacitively-coupled plasma discharge models for mid-range pressures (0.1 - 1 Torr). The verification process involved using the method of manufactured solutions to assess Zapdos spatial and temporal error convergence. L2 errors ranged from 10−2 to 10−4, while the convergence's slope were in agreement with the predicted slopes for the tested variable and time integration orders. The benchmarking process involved comparisons to previously results from the validated finite element code, LSODI [1–3]. These works included 1D and 2D simulations for a range of plasma parameters (densities, temperatures, voltage, etc.). For the 1D cases, Zapdos and LSODI results were in very good agreement. In the 2D cases, variable behaviors matched, with slight discrepancies in peak values. The validation process involved comparisons to experimental works including electron density measurements by microwave interferometry [4] and metastable density measurements by planar laser-induced fluorescence imaging [5]. Results shown reasonable agreement at higher pressure, with results starting to diverge at low pressures. Probable causes for this diverges are the limitation of the fluid assumption for plasmas at low pressure, or the need for more robust boundary conditions. Overall, Zapdos shown reasonable results for the verification, benchmarking, and validation efforts, and Zapdos can be downloaded at Program summary: Program Title: Zapdos CPC Library link to program files: Developer's repository link: Licensing provisions: LGPL-2.1 Programming language: C++, Python Supplementary material: Nature of problem: For the plasma computational community, multiphysics packages are needed for the highly couple physics seen in plasma problems (e.g. chemistry, fluid flow, heat transfer, electromagnetic, etc.). One limiting factor for these types of computational research is the high cost to purchase the licenses needed for established multiphysics packages, such as COMSOL. An additional problem that can arise is the limited ability to add new physics to these existing frameworks, in such a way that new physics can be easily coupled to current models. For any new software that wants to tackle these problems, the question of verification and validation for these codes needs to be addressed. Solution method: Zapdos is an open-source finite element plasma fluid solver based on the MOOSE multiphysics framework. MOOSE (Multiphysics Object Oriented Simulation Environment) solves highly nonlinear, tightly coupled sets of partial differential equations (PDEs) and houses multiple physics applications that can be easily coupled together. Zapdos, along with the MOOSE ecosystem, is all free, open-source, and completing customizable with no black box components. Zapdos has gone through verification and validation for applications common in the plasma computational community. Additional comments including restrictions and unusual features: Zapdos, along with MOOSE and other MOOSE applications, require an Unix based operating system.

Original languageEnglish (US)
Article number108837
JournalComputer Physics Communications
StatePublished - Oct 2023
Externally publishedYes


  • Finite element method
  • Fluid approximation
  • Method of manufactured solutions
  • Open-source
  • Plasma
  • Verification and validation

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy


Dive into the research topics of 'Verification and validation of the open-source plasma fluid code: Zapdos'. Together they form a unique fingerprint.

Cite this