Development and testing of high-resolution upwind schemes

Development and testing of high-resolution upwind schemes

Upwind schemes for incompressible free surface flows

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The correct modeling of convection processes, without introducing excessive artificial damping while retaining reasonable accuracy, stability, boundedness, and algorithmic simplicity, plays a key role in reproducing complex flow physics. In this book, we present the development and testing of high-resolution upwind schemes for controlling the numerical diffusion in general conservation laws and fluid dynamics problems. In particular, the ALUS (Adaptive Linear Upwind Scheme) and TOPUS (Third-Order Polynomial Upwind Scheme) are developed. These schemes are tested in 1D scalar transport, 1D conve...