how to ensure positivity & boundedness of converged solution of scalar unknown like mole fraction of a hyperbolic partial PDE?

Hyperbolic partial differential equations are encountered in systems like packed bed reactor. Solvers give converged solution but sometimes the solution for unknown scalar variable like molefraction is predicted to be negative instead of remaining bounded in the interval of 0 to 1. Setting this to zero and using zero value for next iteration corrupts the mass balance closure. Is finite volume method based on flux-limiters the only way to get over this problem or is there any other computationally simple method?

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