Solution of some problems of pollution motion in subsoil waters under groove hydroconstructions (Q2703280)

The paper deals with the mathematical model of pollution motion under groove hydroconstructions. The corresponding initial-boundary value problem has the form NEWLINE\[NEWLINE\sigma{\partial C\over \partial t}= D\Delta C-\vec\nu(x,y)\nabla C+ f(t,x,y),\quad \Delta \phi=0,\quad x\in {\mathbb{R}},\;y\in (0,T),\;t>0,NEWLINE\]NEWLINE NEWLINE\[NEWLINEC(x,y,0)=C_{0}(x,y),\quad C(x,y,t)|_{\Gamma}=g(x,y,t), \quad (\partial C/\partial n)|_{\Gamma_{1}}=0,NEWLINE\]NEWLINE where \(C\) is the concentration of the substance; \(\sigma\) is the active porosity of the surroundings; \(D\) is the coefficient of convective diffusion; \(\vec\nu\) is the vector of filtration velocity; the function \(f(t,x,y)\) describes the sources and flows; \(\phi\) is the potential of filtration velocity; \(n\) is the external normal vector to the boundary of the filtration region. The author considers two types of boundary: NEWLINENEWLINENEWLINE1) \(\Gamma=\{(x,y)|y=0, x\in(-\infty,-l_{1})\cup (a,b)\cup(l_{2},\infty)\}\), \(\Gamma_{1}=\{(x,y)|y=0, x\in(-l_{1},a]\cup[b,l_{2})\}\cup\{(x,y)|y=T, x\in {\mathbb{R}}\}\); NEWLINENEWLINENEWLINE2)\(\Gamma=\{(x,y)|y=0, x\in(-\infty,-l_{1})\cup (a,b)\cup(l_{2},\infty)\}\cup\{(x,y)|y=T, x\in {\mathbb{R}}\}\), \(\Gamma_{1}=\{(x,y)|y=0, x\in(-l_{1},a]\cup[b,l_{2})\}\). NEWLINENEWLINENEWLINEA monotone difference scheme is constructed to find an approximate solution of the problem.