Numerical resistivity
Encyclopedia
Numerical resistivity is a problem in computer simulation
s of ideal magnetohydrodynamics
(MHD). It is a form of numerical diffusion
. In near-ideal MHD systems, the magnetic field can diffuse only very slowly through the plasma
or fluid
of the system; it is rate-limited by the resistivity
of the fluid. In Eulerian simulations where the field is arbitrarily aligned compared to the simulation grid, the numerical diffusion
rate takes the form similar to an additional resistivity, causing non-physical and sometimes bursty magnetic reconnection
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 and inner heliosphere
, this numerical effect can be several orders of magnitude larger than the physical resistivity of the plasma.
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
s of ideal magnetohydrodynamics
Magnetohydrodynamics
Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
(MHD). It is a form of numerical diffusion
Numerical diffusion
Numerical diffusion is a difficulty with computer simulations of continua wherein the simulated medium exhibits a higher diffusivity than the true medium...
. In near-ideal MHD systems, the magnetic field can diffuse only very slowly through the plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
or fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
of the system; it is rate-limited by the resistivity
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
of the fluid. In Eulerian simulations where the field is arbitrarily aligned compared to the simulation grid, the numerical diffusion
Numerical diffusion
Numerical diffusion is a difficulty with computer simulations of continua wherein the simulated medium exhibits a higher diffusivity than the true medium...
rate takes the form similar to an additional resistivity, causing non-physical and sometimes bursty magnetic reconnection
Magnetic reconnection
Magnetic reconnection is a physical process in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration...
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 and inner heliosphere
Heliosphere
The heliosphere is a bubble in space "blown" into the interstellar medium by the solar wind. Although electrically neutral atoms from interstellar volume can penetrate this bubble, virtually all of the material in the heliosphere emanates from the Sun itself...
, this numerical effect can be several orders of magnitude larger than the physical resistivity of the plasma.