Most of the physical phenomenon that occurs in nature or in systems engineered by humans, do not present the ideal case scenarios usually dealt with in the classrooms. Chemical industry is rich in diverse applications that have evolved overtime through human experimentation and experience and have eluded the complete understanding possible within the known boundaries of science. It is a constant endeavour of computational scientists to bring these phenomena within the reach of science and make accurate predictions of the system behaviour over an extended period into future. This treatise is one such humble attempt at bringing the ever confounding physical environment we live and interact with, into comprehension. This book is targeted towards the computational scientists working in the area of computational physics and numerical analysis. It starts with the first principles of conservation and develops a numerical technique to solve the fully transient coupled partial differential equations describing motion of solids in fluids. It also presents a simple approach to collision modeling between rigid bodies and practical application of the method in solving real life problems.