Code-Verification Techniques for Collisional Plasma Dynamics
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Particle-in-cell methods are commonly used in computational plasma physics. These methods solve kinetic equations for the particles and are typically coupled with electromagnetic field equations. These methods yield many code-verification challenges due to the various sources of numerical error and their possible interactions. For computational physics codes in general, it is necessary to establish the credibility of the simulation results. This is typically accomplished through verification and validation. Validation evaluates the appropriateness of the models instantiated in the code for representing the relevant physical phenomena, and is typically performed through comparison with experimental data. Verification, on the other hand, assesses the correctness of the numerical solutions produced by the code, through comparison with the expected theoretical behavior of the implemented numerical methods. Verification can be further divided into the activities of code verification and solution verification. Solution verification involves the estimation of the numerical error for a particular simulation, whereas code verification assesses the correctness of the numerical-method implementations. Code verification is the focus of this work. In general, codes that approximately solve systems of differential, integral, or integro-differential equations can only be verified by using them to solve problems with known solutions. The discretization of the governing equations necessarily incurs some truncation error, and thus the approximate solutions produced from the discretized equations will incur an associated discretization error. If the solution to the problem is known, a measure of the discretization error may be evaluated directly from the approximate solution. The code may be verified by examining the rate at which the error decreases as the discretization is refined, thereby verifying the observed order of accuracy of the discretization scheme is the expected order of accuracy. Code verification has been performed for several physics disciplines; however, existing literature contains few instances of MMS being used in the verification of software for computational plasma dynamics, especially with collisions. In this work, we present our code-verification progress for collisional plasma physics.
