The convection term is often written as, where the advection operator is used.
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The nonlinearity of the convection term is the main problem in solving a stationary or nonstationary Navier-Stokes equation or Euler equation problems.
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This scheme is used to solve convection diffusion equations using second order central difference for the diffusion term and for the convection term the scheme is third order accurate in space and first order accurate in time.
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In addition to the wide range of length and time scales and the associated computational cost, the governing equations of fluid dynamics contain a non-linear convection term and a non-linear and non-local pressure gradient term.
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In fact neglecting the convection term, incompressible Navier Stokes equations lead to a vector diffusion equation ( namely Stokes equations ), but in general the convection term is present, so incompressible Navier Stokes equations belong to the class of convection-diffusion equations.
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In fact neglecting the convection term, incompressible Navier Stokes equations lead to a vector diffusion equation ( namely Stokes equations ), but in general the convection term is present, so incompressible Navier Stokes equations belong to the class of convection-diffusion equations.
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