Abstract
Chapter 2 is an introduction to numerical modeling of diffusional transport by means of finite-difference schemes. By focusing on scalar equations, emphasis is placed on the properties of the numerical schemes and the prediction of the associated errors. The behavior of parasitic waves in numerical solutions is examined in view of the concepts of dissipation, dispersion, and group velocity. Selective numerical dissipation is used to remove spurious oscillations while leaving unaffected longer, true waves. Explicit and implicit finite-difference schemes are constructed including the FTCS and BTCS methods. Essential and natural boundary conditions are formulated and point sources are approximated. Accuracy, stability, and consistency issues are discussed in the context of the Leap-Frog, DuFort-Frankel and Crank-Nicolson methods.
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