Using Analytical Solutions For Homogenous Soils To Assess Numerical Solutions For Layered Soils
نویسندگان
چکیده
Analytical solutions for non-steady flow are an important aspect of mathematical modeling in all fields of computational science. An analytical solution provides an exact solution for a specific (simplified) test case, which then can be used to test and verify numerical solutions. Within soil physics, there has been a multitude of analytical solutions that model transient flow through onedimensional homogenous soil profiles under various flow conditions. For homogenous soils, analytical solutions exist for realistic soil types (i.e. non-linear hydraulic functions) and for coupled solute and water transport. However, for layered soils, there has only been one analytical solution for non-steady flow. Even though this solution has been useful for testing numerical schemes, the disadvantages of the solution are 1) it is lengthy, complex and difficult to program; 2) is only valid for a particular form of the hydraulic functions with a constant hydraulic diffusivity (D); and 3) one of the key soil parameters is constant across soil layers.
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