Governing Equations

TL;DR: The paper describes a numerical method for modeling solar-wind physics, focusing on the interaction with planets and comets. The method employs a collocated finite-volume approach based on a Roe-type approximate Riemann solver with adaptive refinement. Results are shown for two cases: interaction with Venus and Halley's comet.

Abstract: In t roduc t ion The solar wind, away from the vicinity of a planet or other body, is a plasma flowing at supersonic speeds. As a body is approached, a bow shock is formed. Behind the bow shock, the flow is decelerated, and the electro-magnetic effects become pronounced, particularly in the case of a magnetized planet such as the Earth. This paper describes a numerical method for modeling solar-wind physics that is as close as possible to modern methods for compressible gas dynamics. In particular, a collocated finite-volume approach based on a Roe-type approximate Riemann solver with adaptive refinement has been developed and used in this work. Two pieces of the scheme the governing equations and the approximate Riemann solver are described in the following sections. Results for two cases are shown: interaction of the solar wind with Venus, and interaction of the solar wind with Halley's comet. For both cases, comparisons of the computations with observations (the Pioneer Venus Orbiter and the Giotto spacecraft) are shown.