In this paper the authors discuss the numerical simulation problem of threedimensional
compressible contamination treatment from nuclear waste. The mathematical
model is defined by an initial-boundary nonlinear convection-diffusion system
of four partial differential equations: a parabolic equation for the pressure, two
convection-diffusion equations for the concentrations of brine and radionuclide and a
heat conduction equation for the temperature. The pressure appears within the concentration
equations and heat conduction equation, and the Darcy velocity controls the
concentrations and the temperature. The pressure is solved by the conservative mixed
volume element method, and the order of the accuracy is improved by the Darcy velocity.
The concentration of brine and temperature are computed by the upwind mixed
volume element method on a changing mesh, where the diffusion is discretized by a
mixed volume element and the convection is treated by an upwind scheme. The composite
method can solve the convection-dominated diffusion problems well because it
eliminates numerical dispersion and nonphysical oscillation and has high order computational
accuracy. The mixed volume element has the local conservation of mass and
energy, and it can obtain the brine and temperature and their adjoint vector functions
simultaneously. The conservation nature plays an important role in numerical simulation
of underground fluid. The concentrations of radionuclide factors are solved by the
method of upwind fractional step difference and the computational work is decreased
by decomposing a three-dimensional problem into three successive one-dimensional
problems and using the method of speedup. By the theory and technique of a priori
estimates of differential equations, we derive an optimal order result in L^{2} norm. Numerical
examples are given to show the effectiveness and practicability and the composite
method is testified as a powerful tool to solve the well-known actual problem.