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Solving complex convection-diffusion equations is very important to many practical mathematical and physical problems. After the finite difference discretization, most of the time for equations solution is spent on sparse linear equation solvers. In this paper, our goal is to solve 2D Nonlinear Unsteady Convection-Diffusion Equations by accelerating an iterative algorithm named Jacobi-preconditioned QMRCGSTAB on a heterogenous platform, which is composed of a multi-core processor and multiple GPUs. Firstly, a basic implementation and evaluation for adapting the problem to this kind of platform is given. Then, we propose two optimization methods to improve the performance: kernel merging method and matrix boundary data processing. Our experimental evaluation on an AMD Opteron(tm) quad-core processor 2380 linked to an NVIDIA Tesla S1070 platform with four GPUs delivers the peak performance of 33 GFLOPS (double precision), which is a speedup of close to a factor 32 compared to the same problem running on 4 cores of the same CPU.