Boundary Conditins amp; Geometry Group边界条件amp；几何组.pptVIP

Boundary Conditions for MHD Deriving Consistent Boundary Conditions for MHD* Boundary Conditions for Ideal MHD Boundary Conditions for Ideal MHD Boundary Conditions for Ideal MHD Boundary Conditions for Ideal MHD Boundary Conditions for Resistive MHD Boundary Conditions for Resistive MHD Boundary Conditions for Insulators Plasma Dynamics Group Aerospace Energetics Research Program Resistive MHD equations in weakly conservative form (balance form, divergence form, flux/source form) are where the total energy is given by Expressing the MHD equations in compact form, Integrating over the domain, For ideal MHD, RHS vanishes. Consistent boundary values must be specified for the normal fluxes in the surface integral. *The discussion is limited to Cartesian coordinates. Additional terms arise in other coordinate systems, e.g. cylindrical. Consider the case of perfectly conducting, impermeable wall For the continuity equation, this gives Density is unconstrained. Typically, extrapolate from domain, or simply For the induction equation, the boundary conditions give If no initial field penetrates boundary, Bn = 0, vt is unconstrained. Typically, extrapolate from domain, or simply If initial field penetrates boundary, Bn ≠ 0, it must be specified and For the momentum equation, the boundary conditions give If Bn = 0, Bt is unconstrained, but net pressure at boundary must be specified. If Bn ≠ 0, B and p must be specified at boundary. For the energy equation, the boundary conditions give No additional constraints are derived. The first term is unconstrained since vn = 0. If Bn = 0, Bt ?vt is unconstrained. If Bn ≠ 0, Bt ?vt must be specified. However, vt = 0 from induction equation. Bt is unconstrained. If the resistive MHD equations are considered, the RHS terms modify the required boundary conditions. For the induction equation, the integral of the RHS gives Need to specify ηjt. If Bn = 0, must be specified. If Bn ≠ 0, must also be specified. If the resistive MHD equatio