  This paper presents a more stable implementation and a highly accurate
numerical tool for predicting flooding in urban areas. We started with the
(linearised) well-posedness analysis by [1], where far-field boundary
conditions were proposed but extended their analysis to include wall
boundaries. Specifically, high-order Summation-by-parts (SBP) finite-difference
operators were employed to construct a scheme for the Shallow Water Equations.
Subsequently, a stable SBP scheme with Simultaneous Approximation Terms that
imposes both far-field and wall boundaries was developed. Finally, we extended
the schemes and their stability proofs to non-cartesian domains. To demonstrate
the strength of the schemes, computations for problems with exact solutions
were performed and a theoretical design-order with second-, third- and fourth
(2,3,4) convergence rates obtained. Finally, we apply the 4th-order scheme to
steady river channel, canal (or flood control channel simulations), and
dam-break problems. The results show that the imposition of the boundary
conditions are stable, and that they cause no visible reflections at the
boundaries. The analysis adequately becomes necessary in flood risk management
decisions since they can confirm stable and accurate future predictions of
floodplain variables
