Numerical errors generated by WENO-based interface-capturing schemes in multifluid computations

When using high-order accurate shock-capturing methods, e.g., weighted essentially non-oscillatory schemes (WENO), numerical errors are often generated in simulations of isolated contact discontinuities and material interfaces when trying to capture these features on a grid. Spurious pressure oscillations are generated at interfaces and contacts propagate through the flow field. In addition, temperature errors may be generated. The present work constitutes an attempt to provide a unifying theory describing these errors. First, contact discontinuities in a single-component fluid are discussed, followed by material interfaces and contact discontinuities separating different fluids. Errors that are generated in simulations of these features are analyzed and means to prevent them are introduced and discussed.