The numerical solution of second-order boundary value problems on nonuniform meshes
Mathematics of Computation
Supra-convergent schemes on irregular grids
Mathematics of Computation
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Support-operator finite-difference algorithms for general elliptic problems
Journal of Computational Physics
Applied Numerical Mathematics
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
Journal of Computational Physics
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
Error Expansion for an Upwind Scheme Applied to a Two-Dimensional Convection-Diffusion Problem
SIAM Journal on Numerical Analysis
Stable and Accurate Artificial Dissipation
Journal of Scientific Computing
A Volume-of-Fluid based simulation method for wave impact problems
Journal of Computational Physics
Journal of Computational Physics
The numerical simulation of liquid sloshing on board spacecraft
Journal of Computational Physics
Journal of Computational Physics
Symmetry-preserving discretization of Navier-Stokes equations on collocated unstructured grids
Journal of Computational Physics
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Although upwind discretization of convection will lead to a diagonally dominant coefficient matrix, on arbitrary grids the latter is not necessarily positive real, i.e. its symmetric part need not be positive definite ('negative diffusion'). Especially on contracting-expanding grids this property can be lost. The paper discusses a conservative (finite-volume) upwind variant for which the latter property is guaranteed to hold, irrespective of grid (ir)regularity. Further, empirically it is found that often its global discretization error is smaller than that of the 'traditional' (finite-difference) upwind method. Finally, it is shown that in many situations its extremal eigenvalues at the outer side of the spectrum move towards the imaginary axis, thus enhancing the stability of explicit time-integration methods.