We present a new optimization-based, conservative, and quasi-monotone
method for passive tracer transport. The scheme combines high-order spectral element
discretization in space with semi-Lagrangian time stepping. Solution of a singly linearly
constrained quadratic program with simple bounds enforces conservation and physically
motivated solution bounds. The scheme can handle efficiently a large number of passive
tracers because the semi-Lagrangian time stepping only needs to evolve the grid
points where the primitive variables are stored and allows for larger time steps than a
conventional explicit spectral element method. Numerical examples show that the use
of optimization to enforce physical properties does not affect significantly the spectral
accuracy for smooth solutions. Performance studies reveal the benefits of high-order approximations,
including for discontinuous solutions
