Analytical Solutions Sample Clauses

Analytical Solutions. ‌ For comparison with numerical solutions, an exact solution may be available in the form of an Analytical Solution to the governing equations. A typical limitation of analytical solutions is that they are available only for physical problems much simpler than the situation of interest; and also terms/physical phenomena may be left uncoupled A key requirement of the test is that it is able to exercise all the relevant terms in the governing equations. For example, running a viscous code at very high Xxxxxxxx number means that the viscous terms will be swamped by the inertia terms; any errors in the implementation of the viscous terms will be severely diluted and may remain unobserved. Identifying a test where (in this case) the Re ≈1 is more appropriate for exercising the main terms. The choice of an appropriate analytical solution will depend on the nature of the physical terms being verified. For example, verification of a compressible flow solver (relevant for H2 detonation) may be undertaken with a Sod Shock tube / Riemann problem, where spatial discontinuities in the flow are a strong test of spatial discretisation accuracy11. Many examples are given in the literature, and worked examples are provided below.
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