Numerical diffusion

This phenomenon can be particularly egregious when the system should not be diffusive at all, for example an ideal fluid acquiring some spurious viscosity in a numerical model.For example, shock waves in fluids and current sheets in plasmas are infinitely thin in some approximations; this can cause difficulty for numerical codes.A simple way to avoid the difficulty is to add diffusion that smooths out the shock or current sheet.Since there are no chemical or thermodynamical reactions during expansion of air in water there is no possibility to come up with another (i.e. non red or blue) phase during the simulation.These inaccuracies between single phases are based on numerical diffusion and can be decreased by mesh refining.
Phasefield Simulation of a airbubble within a phase of water
computer simulationsfluidsdiffusivityEulerian simulationsdifferential equationsNavier–Stokes equationdiscretizedfinite-difference equationsdiffusivemagnetohydrodynamicsingularitiesshock wavescurrent sheetsplasmasmomentumnumerical resistivityPhasefield-problemFalse diffusionNumerical dispersionNumerical error