Numerical resistivity is a problem in

computer simulation Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...

s of ideal

magnetohydrodynamics Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, ...

(MHD). It is a form of

numerical diffusion Numerical diffusion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher diffusivity than the true medium. This phenomenon can be particularly egregious when the system should not be ...

. In near-ideal MHD systems, the magnetic field can diffuse only very slowly through the

plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...

fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...

of the system; it is rate-limited by the inverse of the

resistivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...

of the fluid. In Eulerian simulations where the field is arbitrarily aligned compared to the simulation grid, the

rate takes the form similar to an additional resistivity, causing non-physical and sometimes bursty

magnetic reconnection Magnetic reconnection is a physical process occurring in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnectio ...

in the simulation. Numerical resistivity is a function of resolution, alignment of the magnetic field with the grid, and numerical method. In general, numerical resistivity will not behave isotropically, and there can be different effective numerical resistivities in different parts of the computational domain. For current (2005) simulations of the

solar corona A corona ( coronas or coronae) is the outermost layer of a star's atmosphere. It consists of plasma. The Sun's corona lies above the chromosphere and extends millions of kilometres into outer space. It is most easily seen during a total solar e ...

and inner

heliosphere The heliosphere is the magnetosphere, astrosphere and outermost atmospheric layer of the Sun. It takes the shape of a vast, bubble-like region of space. In plasma physics terms, it is the cavity formed by the Sun in the surrounding interstell ...

, this numerical effect can be several orders of magnitude larger than the physical resistivity of the plasma.

See also