Strong Stability Preserving Runge-Kutta Methods Applied to Advection- Diffusion Problem

Resumo

Heat transfer phenomena are related to several applications in different scientific branches. Advection-
diffusion problems with spatial properties variation describe the wave development associated with a physical

change in heterogeneous media or multi-layered materials, such as laminated media or conjugated problems. Fur-
thermore, an incompressible thermally developing laminar flow with hydrodynamically developed fluid, known as

the Graetz problem, is a typical example of this phenomenon . However, the fluid property variation imposes some
mathematical challenges to predict accurate solutions. The Strong Stability Preserving (SSP) methods are capable
of numerical schemes to increase their accuracy order while maintaining the original stability properties from their

generator Euler method. This methodology is developed basically by rewriting the multistage scheme as a combi-
nation of steps in the Euler method and introducing a time step barrier. On the other hand, the Generalized Integral

Transformation Technique (GITT) is a hybrid numerical-analytical approach that provides an infinite system of
coupled ordinary differential equations (ODE) that needs to be solved numerically by truncating the expansion.
Indeed, GITT consists of this solution procedure characterized by a hybrid analytical-numerical nature. Therefore,
the present work studies the SSP Runge-Kutta schemes compared to the GITT to solve the Graetz problem in the
absence of the axial diffusion.