What is numerical dispersion in reservoir simulation?

What is numerical dispersion in reservoir simulation?

Standard finite difference methods used in reservoir simulation employ large amounts of numerical dispersion. Numerical dispersion can, in addition to smearing fronts, cause their shapes to be severely distorted. This phenomenon is commonly referred to as the grid orientation effect.

What is dispersion in numerical methods?

In computational mathematics, numerical dispersion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher dispersivity than the true medium. For these reasons, it is often seen as a numerical error.

What causes numerical dispersion?

Numerical dispersion occurs when a higher order discretisation scheme is used to improve accuracy of the result. This is due to the truncation error of the discretisation. If the truncation is an odd-order method (such as the first order unwind method) the leading truncation error is even.

How can we avoid numerical dispersion?

A simple way to avoid the difficulty is to add diffusion that smooths out the shock or current sheet. Higher order numerical methods (including spectral methods) tend to have less numerical diffusion than low order methods.

What is the difference between dispersion and dissipation?

To clarify, dissipation is the function of wave dying in magnitude, while dispersion is when the speed of the propagating wave is not calculated with proper accuracy and it “lags” behind the actual function.

What is dispersion in CFD?

Dispersion is the combined effort of adveciton and diffusion.

What is the problem of numerical diffusivity?

Numerical or false diffusion is the phenomenon of inserting errors in the calculations that compromise the accuracy of the computational solution. The Taylor series analysis that reveals the truncation/discretization errors of the differential equations terms should not be termed as false diffusion.

What is CFD diffusion?

CFD Open Series. Diffusion is a physical process that occurs in a flow of gas in which some property is transported by the random motion of the molecules of the gas. Diffusion is related to the stress tensor and to the viscosity of the gas.

What is dissipative energy?

Dissipation is a term that is often used to describe ways in which energy is wasted. Any energy that is not transferred to useful energy stores is said to be wasted because it is lost to the surroundings. In a mechanical system, energy is dissipated when two surfaces rub together.

Why is numerical dispersion an artifact of FDTD?

Numerical dispersion is an artifact resulting from the discrete spatial sampling of the FDTD mesh. This means that for a coarse mesh, the speed of light on the FDTD mesh may depart slightly from the exact value of the speed of light in the material being simulated.

How is the non uniform mesh used in FDTD?

The automesh feature automatically configures the non-uniform mesh to minimize the effects of numerical dispersion. In the usual use case, the user simply chooses a setting on the accuracy slider, which ranges in value from 1 to 8.

What is the critical parameter for numerical dispersion?

The critical parameter that affects numerical dispersion is N = lambda_0/ (n D) where lambda_0 is the free space wavelength, n is the refractive index and D is the FDTD mesh cell size. N represents the number of mesh cells per wavelength, and the numerical dispersion artifact becomes negligible as N becomes large.

When does dispersion occur in a numerical model?

This phenomenon can be particularly egregious when the system should not be dispersive at all, for example a fluid acquiring some spurious dispersion in a numerical model. It occurs whenever the dispersion relation for the finite difference approximation is nonlinear. For these reasons, it is often seen as a numerical error .