An improved numerical scheme for coffee Extraction Yield evaluation

This work proposes a polynomial-augmented radial basis function (RBF) collocation method with polyharmonic to solve the advection–diffusion–reaction (ADR) equations associated with the percolation process for espresso extraction. Numerical methods for solving these equations are useful for many applications where we have chemical reactions and transport in a porous medium. Polynomial augmentation in RBF collocation is useful when it is also necessary to approximate the derivatives, to overcome the stagnation error problem. Moreover, the polyharmonic RBF avoids the hassle of determining the shape parameter. The proposed meshless method allows for discretising the ADR equations and obtaining a numerical solution used to evaluate the efficiency of the extraction process in espresso coffee; this method can be easily generalised to higher dimensions or more complex domains. The numerical results have been compared to measurements carried out in the laboratory. • Numerical scheme for the solution of Advection–diffusion–reaction problems. • Prediction of the amount of total dissolved solids extracted in the espresso coffee percolation process. • Radial basis functions are used to approximate the spatial derivatives. • Comparison of the numerical results with experimental ones.